How much of a safety concern is the rust on the underside frame of my 2000 Chevy Cavalier?
Big, rust is always deeper than you can see. If it’s on your car’s frame, that means your frame will not provide the best protection in case of an accident
Edit: how did I finish typing before @Mustangman???
Without seeing pictures of where the rust IS, that is impossible to answer. If you had it in a shop and they told you it was serious, believe them. But get a second shop’s opinion.
Rust and Icebergs have the same appearance. You only can see about 1/3 of it. Take this to a body shop ( they are now called Collision Centers ) and get a real assessment instead of web guesses from people who cannot see the vehicle. This is a safety problem for you and people who share the road with you.