Very generally speaking, a divorce case starts when one spouse files what is called a "Complaint for Divorce". Once the Complaint is filed, then the filing spouse must formally serve a copy of the Complaint on the other spouse in order to proceed with the case. The case ends when the parties either come to an agreement on all the issues (often at mediation), put that agreement into a written document called a Judgment of Divorce, present the Judgment to the Judge and the Judge signs the Judgment. Alternatively, the parties have a trail, the court (judge) makes its decision and then it signs the Judgement of Divorce and provides notice of its decision to the parties. In either case, the parties are not divorced until the Judge signs the Judgment.
Some family law cases take an unfortunately long time, it is a slow process and complications in a case can make it a very slow process. Sometimes, a spouse will pass away due to illness, accident or suicide before the divorce is finalized as described above. If that happens, then the case is dismissed and the living spouse is considered the surviving spouse for the purposes of the marital estate. In which case, all of the property of the parties typically passes directly to the surviving spouse regardless of what agreements or interim orders may have been entered in the divorce case. Even if the parties have mediated the case and reached a written or recorded mediation agreement (which would typically be enforceable and either party could enter a Judgment based upon the recorded agreement over the objection of the other party) on every single detail of the divorce and presented a written judgment signed by the parties and the attorneys to the court, the case will be dismissed and go to probate as described above, if the judge did not sign it before the party passed away.
Now for a final twist, the Michigan Court of Appeals has decided that if the Judgment has been signed and entered by the court but one party appeals, then the case will still proceed as a divorce case but an estate will have to be opened and an administrator (executor) must be appointed to represent the deceased spouse's estate in the appeal. If this occurs, then the Judgment will stand and the surviving spouse will not stand to inherit all of the deceased spouse's property.. Instead, once the court of appeals either affirms the lower court or makes adjustments, then the surviving spouse will receive whatever the court determines is equitable and the estate of the deceased spouse will take that spouse's share. Finally, if the party receiving alimony passes away, then alimony stops, but, if the spouse paying the spousal support passes away, the estate may be ordered to continue paying spousal support to the surviving spouse.