In Minnesota, a spouse may be told to pay maintenance during a divorce. Called both "alimony" and "spousal support" in other areas, this is simply money paid by one spouse to help support the other. It's often used when that spouse was expecting to be supported and can't do so alone.
For example, if one spouse had a job, gave it up to get married and start a family, and cannot get back into the workforce 10 years later, maintenance may be requested.
However, after the divorce, that person may begin dating someone else. If he or she starts living with that person, the spouse who is paying can ask for the payments to be modified or canceled entirely. The idea here is that the new partner may be supporting the person, and there's no need for two people to do it.
It's worth noting that the two don't have to get married for the other spouse to ask for a change. In fact, one of the main things that the court looks at is if the two are only refraining from marriage so that those payments don't stop. If they are, then they're just doing it for an unfair financial advantage.
This does not mean that all requests for modifications are going to be granted. The court isn't likely to make alterations that last for years just because your ex went on a date. However, as relationships change and things grow serious, it's important to know what options you have to make sure the divorce agreement and the court orders are still fair.
Source: Revisor, "2016 Minnesota Statutes," accessed Oct. 27, 2016