I think for the most part you'll be fine. For all intents and purposes you're "borrowing" the car -even if its for a long-term period- the car's "owner" is in another state, sure, but it's not YOURS. And since it's not yours you can't register it in another state and the car's owner can't register it in a non-residence state.
The "most" trouble I think you'd get in is if the police or someone notice a non-state car parked in the same place for a long period of time. (Be it your driveway or apartment parking lot, whatever type of residence you live in.) Then you might get a ticket in which case you go to the traffic court, explain that it's not your car and you're borrowing it from out-of-state owners. Either the ticket will be dismissed or you'll pay an annoying fine, more likely the former.
To cover all of your bases in this regard, I might suggest getting a notarized letter from the car's owner explaining the situation that you can show the police should you have any trouble.
But, largely, you'll be fine. I know a guy who kept his car registered in a neighboring state under his parents' address because the personal-property taxes were lower over there. He lived on this side of the state for several years on these out-of-state plates for years without any problems.
I know another guy who drove on expired tags for almost six months before getting them re-newed, no problems. (Aside from fines, late fees, when he finally went to the DMV to renew.)
You should have no trouble at all, Kestra. Good luck with what is going on with your life and hope it gets better for you.