The Old Testament managed the marital contract through clear rules and laws. "If he takes another wife, he shall not diminish her food, her clothing, and her marriage rights. And if he does not do these three for her, then she shall go out free, without paying money." (Ex 21:10-11) Here are clearly seen main generic rules how the husband should maintain his spouse. Although nowadays it is not what we usually observe. In ancient family breaking these elementary rules already was a reason to break the marriage. Of course, here are included other things, like abandoning family provisioning or undermining it with the laziness, deliberate sabotage of certain agreements, psychological pressure in order to gain something, various manipulations etc. Of course, loyalty and faithfulness should remain indestructible.
But at the same time, the law of the Old Testament was quite limited as well, as it was built on common rules and common regulations, that have been applied to all people without exceptions. Since such law was not an universal truth that could be always helpful through all the time and places in every situations, just like any other law, it is also quite vulnerable by individual corner cases, exploiting logical or factual holes in it. For example, while the wedding ceremony itself is trying to guarantee some duties and is trying to bring some obligations, however it cannot guarantee honesty and true intentions of another person. Technically, if promises sound decorous and auspicious, the cheerful overjoyed response on them is related more to the ceremony itself, rather than to the real practical life. For this reason it is possible to say a promise without actually giving it. One can speak anything the ear would like to hear and one can allege any promises that sound sweet. But will they be actually fulfilled and accomplished in the real life? And when the couple after some time decided to divorce, the given promises reveal empty and useless.
However, Christ did not come to Israel in order to improve the law of the Old Testament filling it up with more rules and strengthen in places where the law is defenseless. Instead, He changed it in the very principle. As we already saw, Jesus clearly taught, that "So then, they are no longer two but one flesh. Therefore what God has joined together, let not man separate." (Matthew 19:6). He, knowing all the hefty weakness of the mankind, never preached impassable utopias which would be preposterous to what actually is feasible to achieve. What exactly taught Jesus, so that would be possible to accomplish by people that are usual, fallible, prone to sin, and often changing their views?
First of all, it is needed to realise the fact that every marriage in the biblical understanding and Jewish culture — is just a normal agreement between two people whose foundation is thorough compliance of the principles and rules of the contract. And such agreement ceases to be valid and considered void if any party discontinue to perform what was required by such contract.
Jesus demonstrated how it is possible to influence certain plans of God through the choice. Of course, the omniscient God knows what a mankind is going to choose and what will happen if the choice will be wrong. So the omniscient God also gives the ability to prevent certain bad things to happen and therefore warns people what choice would be better to make. If there would be no such possibility to choose and everything would be foreseen and pre-destined, then by definition mankind could not separate anything what God has been joined together and thus such statement from Jesus would be meaningless and even detrimental to His teaching. Therefore the power of the impact by a human influence lays in the pretty simple principle: to follow God, or not. That means, either behave according to how God would wish that, or do something else. Knowing that God συζεύγνυμι (joined) two people for His glory and service, the deliberate breaking of such joint can be just a decision to stop following God at least by one spouse in the marriage. Such person would no longer do what God would like him to do, but would do what is decided by the person. Note that "God made union of two" and a "physical marriage" are tightly coupled phenomena, where serving God keeps two partners in a certain graceful realm, which supports physical marriage. Therefore the destruction of such basis won't necessarily have an immediate impact on the quality of the physical marriage, and therefore a happy and calm life can still continue very long and even last forever. However, such couple is no longer συζεύγνυμι (joined) by God. They are still joined, but already by something else and for something else. This is exactly the hard-heartedness, which Jesus has been mentioned, answering divorce allowance in the law of Moses. This very hardness, turning away form God, turning one's heart into a stone, going by other life choices than God would plan is exactly that gap, break or tear down of the marriage. A true Christ's follower wont persistently violate given promises and by this bringing own relationships to their end. Therefore Jesus meant spiritual support of relationships that are happening in this physical world: "Let man do not separate what God has joined (συζεύγνυμι)". Also interesting the fact that adjective "put together" (συζεύγνυμι) is written in complete form, while infinitive aorist "separate" (χωρίζω, "chórizó", pronounced as "kho-rid'-zo") written by Matthew in uncertain form. That would mean that theoretically one can separate unlimited times. Human tendency to make mistakes and errors and then fix them would explain that. In theological sense it would be to sin and to repent then. This can lead to the conclusion that Jesus calls people to come to their Father, to be with Him and listen to him all the time, correct their mistakes and always return to Him, so that way one would make right daily choices, avoiding major mistakes, and thus keeping a God paired marriage.
In any case, the violation of the marital agreement can be solved in two ways: either transgressions are stopped and the contract can continue operate, or the opposite. Negligence and violations of agreements can be stopped when the offender changes his behaviour and remains compliant. Since marital agreement remains in act, both sides are obligated to continue it. Conversely, the contract considered terminated, if at least one of partners regularly breaking something. As in any other contract, either side can report about its ending, however the responsible is who actually broke its agreements.
Speaking about already mentioned hardness of the heart or "stone heart", it can be defined as cold, insensitive, cruel, callous, stubborn character, although it is not necessary to fully possess all those attributes at once. It also does not mean that tough-looking people immediately must be as such. As well it does not mean that smiling, quiet and kind looking people cannot be despotic dictators, having cruel and selfish intentions deep down in their hearts. There is a widespread allegation that a Christian cannot have hard heart or hard-heartedness, because God promised that "I will give you a new heart and put a new spirit within you; I will take the heart of stone out of your flesh and give you a heart of flesh" (Ez. 36:26).
Based on the principle that Christ cleanses His Church and changes it in His own image, it is important to see that this principle is a daily process of changing of each member of the Church. Such process actually can be initiated only by a good will, voluntarily, from the Church side. This process as such, is a fact that the change into the image of Christ has not finished, but only began, otherwise such process would be redundant. Anyone, who decided to follow Christ can initiate such process, which theologically is called "reflection of Christ". Thus the real changes are only yet to come, since physically nothing has been changed since moment of repentance and the mind only directed towards the expected changes. Character, habits, world view etc — all this still remains with no difference. However, the mere possibility of such process still does not mean its actual existence, since while it is possible to agree with ongoing changes, yet refuse to actually start achieving them. Furthermore, even such process already exist and happens, such fact still does not measure its condition, extent and quality. It is still possible to make an impeccable outward impression to build an imposing image, but this is all about it. Closest example of such condition would be Judas Iscariot — a man, who saw Christ, walked with Him. However he anyway did an irreparable mistake. This is why Ezekiel continues: "I will put My Spirit within you and cause you to walk in My statutes, and you will keep My judgements and do them." (Ez 36:27). The key to understand this phrase is to fulfill the resolutions by actually doing so. And cold, insensitive and stubborn person by definition cannot walk in God's statutes and keep His judgements in full sense of it. If a proposition that hard-heartedness is in principle impossible among Christians is true, then Paul would not call to "work out your own salvation with fear and trembling" (Phil. 2:12), where the keyword is the same as Ezekiel writes: to fulfill. Paul does not write about a kind of animal fear of Hell for self-preservation. Instead, he writes about the fear to lose the close relationship to God. So the internal, private relationship of the couple is an exclusive qualitative internal state of each spouse. And the deeper and more serious process of reflecting character of Christ on people, the better and closer will be relationships of partners that have the common goal to serve God. All of this is impossible to shape to the perfection using law or traditions or rules or prohibitions or regulations etc. As it is also impossible to guarantee a prevention of any wrong decision, made by another partner, since a free choice is an ability of everyone. Instead, each partner should follow the idea to work out agreed own obligations with fear and trembling so the true relationship is not broken and lost. If there would not be a possibility to abandon salvation by neglecting fulfillment of statutes, then there would be no need in a clear, serious warning about that. Consequently, the claim that a Christian cannot have a stone heart or hardness or be cruel, and therefore cannot lose his salvation is false.
Unfortunately, the fate of divorce hit the Creator Himself. Actually, even God is literally divorced! And not just that somebody decided to divorce Him without Him knowing that, but He Himself initiated the process. When reading Jeremiah second and third chapters or Hosea second chapter, then it is clear that God made a covenant with Israel. "And it shall be, in that day, Says the Lord, That you will call Me ‘My Husband,’ And no longer call Me ‘My Master‘" (Hos 2:16). So what happened next? Israel decided the otherwise and broke the contract, by violating its conditions. Therefore God issued a divorce letter to Israel as it is written in Jeremiah: "Then I saw that for all the causes for which backsliding Israel had committed adultery, I had put her away and given her a certificate of divorce; yet her treacherous sister Judah did not fear, but went and played the harlot also." (Jer 3:8) Moreover, God did not forget and recalled that: "Thus says the Lord: 'Where is the certificate of your mother’s divorce, Whom I have put away? Or which of My creditors is it to whom I have sold you? For your iniquities you have sold yourselves, And for your transgressions your mother has been put away." (Is 50:1).
As God says Himself: "because they did not continue in My covenant, and I disregarded them, says the Lord." (Heb. 8:9) so it is valid to assert that breaking an agreement is means its complete destruction rendering it void.