This one is driving me nuts. There was a racing game for windows, I believe from the early 2000's (give or take a few years as an error margin) and the internet doesn't seem to remember it. I say that because I looked for every extensive list of pc racing games I could find and I couldn't find the game! At least I couldn't see a name on a list that ringed a bell...
It was a graphically simple game, but one with very realistic physics. If your wheel fell off, you would have trouble getting traction from that wheel because there truly was nothing pushing the car in that point and everything would act accordingly. At no point in the game you'd get a "you lost your car". You would be the judge of the car's ability to continue (you could pause and quit/retry if you felt it was inpractically damaged).
It had several game modes besides regular racing, for example I remember there was a mode where you needed to travel through "gates" (between posts) in the right order, etc. The approach to the game's racing track was kind of open world, you could drive anywhere the physics allowed with no invisible walls that I can remember. There was more than one type of car, as I remember there being buggies and atvs. The closest screenshot I can find is from an iOS game, maybe it can help (the game looked worse than this):
edit: Found it! Spent a lot of time searching. The name appeared in a list of games people were naming to help someone find a game and I instantly recognized... "1nsane" is the name.