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 $1 USD.
I believe ethereum would survive a virtually complete bitcoin crash. Due to ethereum's survival more likely than not a handful of ERC-20 and ERC-721 tokens could ride the waves and stay strong. Most of the other ethereum tokens would probably be functionally extinct or faint shadows of what they had been.
In this scenario I would imagine gridcoin being one of the best surviving PoW/PoS coins. Its community is one of the most loyal that I know of and there is the utility of citizen science backing gridcoin.
If we talk about the worst case scenario then to me it will be the collapse of crypto market.
First of all it is almost impossible that bitcoin will hit zero or 1$ and why it is impossible to hit bitcoin zero because following must be happened.
All the countries joins together to enforce the ban on bitcoin.
All the countries start to crack the bitcoin holders.
Bitcoin develop a bug that its developer unable to solve.
If this scenario is developed then what will happened.
Bitcoin holders will lose all their investment.
Crypto currencies will lost their complete trust and as a result all the currencies will become to zero.
I'm no expert on cryptocurriencies but the only ALT Coin that would probably survive a crash like that will be TETHER. Tether was designed to be always pegged around a dollar $1, so even if BTC crashed like in your hypothetical scenario or skyrocketed back to $20000, Tether's market price will always be(or tries to) be around $1.
Those would have to be coins that either can stand on their own, or have a completely independent community.
For me I would say....
If Bitcoin was to crash to a dollar, which is incredibly unlikely, I think we would see the death of something like 99% of all of the other coins.