Flat tire

will letting the car stay on the flat (really flat, all the way gone) ruin the rim? I have a 2001 Avalon

Stay ?
Parked in the driveway ? no problem.
Driving on it ? maybe. Aluminum rims can’t take as much punishment as steel. Super slow is better for the wheel than faster.

The rubber will cushion it likely. It will ruin the tire if its repairable.

No, it will not ruin the rim. Assume the tire is no longer usable.

It’s OK to sit, but driving on it could bend the rim and keep you from seating a new tire properly.

I saw a guy drive on a flat tire until he was all the way down to the rotor. Just sitting should not hurt the rim.