Crushed or flattened would be the most common verbs for this. It doesn't require any other words because when you are speaking about a cushion or something similar, it's assumed that it will not become soft again. ;)

Interesting question - I don't think there is a standard idiom, but you could say, it has been "permanently compressed/squashed/flattened/indented" or "it is permanently sagging" or "it has permanently sagged." I can't think of a good alternative to permanent in these examples, though I guess "long-term" or "irredeemably" or "irrecoverably" might work e.g. "it is irredeemably squashed", or "it has been long-term flattened" or "it has been irrecoverably flattened."