If bitcoin crashed to $1 USD I think several altcoins would be flippening. One of the major factors I imagine that would determine whether an altcoin survives or perishes when bitcoin is $1 USD would be how strong the community behind the altcoin is. The other major factor I would consider is how fast bitcoin crashes to $1 USD. The slower the better. If the price of bitcoin drops thousands of dollars within two or three hours there would be panicked selloffs and hasty bitcoin trades for other altcoins not dropping in price as quickly. If the bitcoin price crash happened any more faster than two or three hours I imagine almost all reputable exchanges would freeze all activity before bitcoin could reach $1 USD.
I believe ethereum would survive a virtually complete bitcoin crash. Due to ethereum's survival more likely than not a handful of ERC-20 and ERC-721 tokens could ride the waves and stay strong. Most of the other ethereum tokens would probably be functionally extinct or faint shadows of what they had been.
In this scenario I would imagine gridcoin being one of the best surviving PoW/PoS coins. Its community is one of the most loyal that I know of and there is the utility of citizen science backing gridcoin.