In Minnesota, if you are not a car owner and you get into a car accident or are not otherwise required to have car insurance, you can still get Minnesota no-fault benefits. These are going to come through the Assigned Claims Bureau.
There is an agreement, largely through State Farm and American Family Insurance, that if you are entitled to no-fault benefits but are unable to get it from someone else, do not have your own insurance, live with someone, were not riding in a car that had its own insurance, then you call the Assigned Claims Bureau.
In this process, an investigator is sent, who will make sure you do not have coverage somewhere else, and if you do not, they will set you up with the Assigned Claims Bureau for coverage.
The risk that you have, especially if it is your children that are applying for benefits, is that if you are found partially at fault for the accident, the Assigned Claims Bureau might ask you to reimburse them from some of the portion of what they had State Farm or American Family pay, so you want to make sure that you were not at fault for the accident. Otherwise, you will want to weigh the risk of trying to take care of medical bills, especially if it is one of your children who needs care.