There is no such thing as "our stack is melting away". There is only "it folds to me in HJ, and I am 8BB effective with the players behind, so this is the range, where jamming is more profitable than folding". And if your hand falls outside that range, then you fold it. It does not matter, how you got to have a 8BB stack. Maybe you were card and situation dead for the last several orbits, and your stack slowly dwindled away. Or maybe you had 30BB until the very last hand, but then you ran AK into TT and lost a "flip" to someone with 22BB.
But regardless, which one it was, your decisions for the rest of the tournament should be exactly the same. There is no such thing as "having to do something", because you have been card dead. If you continue to be card dead and have to fold, then eventually your stack will get so short, that its correct to get it in with any two cards from the big blind. And then of course you do this. But not before its correct. A tournament should be played hand for hand.