Ostensibly, any NIL contract would be separate from the university, I understand, so it would be up to the car dealer or whoever to enforce any contract.
Real NIL money from an actual company seeking to use an athlete's name, image, and likeness for actual promotional purposes, wouldn't be tied to the university at all, and in the case of big-time sponsors, would likely travel with the athlete from school to school. For example Quinn Ewers signed several NIL deals with various companies to promote their products, when he went to Ohio State. When he made the move from Ohio State to Texas, he retained those sponsors. Local brands wouldn't necessarily decide to re-up or follow an athlete, but national brands can do, and have done.
But much of the NIL money (and I'd opine, MOST of the NIL money) is coming from collectives that aren't officially tied to the university, but in reality, of course they are. A Tennessee NIL collective will have no interest in paying a player headed to UCLA, for obvious reasons. Most of the current deals are written as 1-year contracts and many of them have specific requirements for appearances or other deliverables, to hold the athlete accountable to the intended purpose of that collective's contract, which is to bind them to the school (but without openly admitting that, of course).
So there probably aren't too many cases of a "real" NIL sponsor using NIL for real purposes of promotion, experiencing an athlete breaching the contract. Maybe a few local car dealerships or restaurants or bail bond services or whatever.
But the major money is either coming from huge national brands like Uber signing Arch Manning, or the university-specific NIL collectives. The former wouldn't have much need to ever attempt to recover damages because there's no reason Uber wouldn't want to follow Arch Manning if he transferred from Texas to Ohio State, but the latter group of wealthy donors definitely would have a desire to pursue collecting damages, in the case of a breach of contract, when an athlete leaves your university early without fulfilling the deliverables in the contract.