Can someone sue you for car damages 4 years later with no police report or insurance claim?

They can file but with nothing to substantiate will not prevail. Just make sure you don't lose by default for not showing up and you have it made.

Keep in mind, though, that a police report is not generated in all cases. Further, the fact that there is not one does not, in and of itself, mean that a subsequent suit will fail. In many jurisdictions, the police report is not admissible in evidence.

Instead, what is crucial is the live testimony of witnesses as to how the collision occurred. The witnesses can be the drivers, passengers, or onlookers. A witness can also be the investigating police officer who can testify to the juxtaposition of the vehicles at the time of his/her arrival at the scene. If the cars were not moved, this can be important evidence as to who may have been at fault for the collision.