No. Parking is leaving your possession somewhere and should apply to the registered owner. It is not illegal to own a car that someone else used to run a red light.
But if you'd like to tell the fall, I'm sure some prosecutors wouldn't dig too hard to find the guilty party.
Edit: subpoena is not a criminal charge afaik is what I’m saying
10 minutes before the murder: Expect to get an accusation of accessory to murder, conspiracy to murder and a few additional tomes of the penal code. We all know you are innocent, but you should better find a good lawyer just in case instead of wasting your last free minutes arguing on the internet.
While a bit more extreme than your example, there have been multiple cases where the parents of a school shooter have been held responsible because they provided access to a weapon when there were warning signs.
On the less extreme end of the spectrum, this is the same reason why you have to pretend that you are buying a "water pipe for tobacco" and not a bong if you don't want to get kicked out of the headshop (in places where that is still illegal).
If they used the car with your permission, you should either be responsible for what they do with it, or be able to point to the person who was using it.
Sure, but I still don't know who they are, so I can't give their name over for either investigating the theft or reassigning the speeding/red light/parking fine.
If your car was magically stolen and returned, and you have no idea that it happened, or who could have done this... Well, that's certainly an interesting legal argument that you could make to a judge. I doubt he'll believe you.