I assume you mean pushing (ie broadcasting) on chain. If you push an old state, say one where you have more Bitcoin than you actually do, all your channel partner needs to do is broadcast the correct version. That’s what ANYPREVOUT does - it allows you to commit/sign a transaction that isn’t bound to any particular previous output, it can be any output. In the this case, the any output it’s binding to is the old (bad) state you pushed.