With the price plummeting I am wondering at what price will Bitcoin not be profitable to mine anymore?
It's not profitable if you just have few ASICs in your home, mining is a big business which require lots of resource and capital to get started.
What is the break-even point?
There is no specific amount for everyone, it's depends on how much you have invested, electricity costs and bitcoin price.
What happens when the price is so low that it costs the miners more to mine BTC than it rewards them? What happens if they pull the plug? BTC is dead then?
Miners will stay for months without profit, maybe 3-6 months or at least a year for a big player. If mining doesn't cover electricity costs, new miners will suffer under a huge losses. But for some miners, it's a natural selection to get rid of incompetent miners and the rest will get more bitcoin.
Bitcoin will never die, not until the nuclear war takes place.
Miners who have no confidence in the prospect of bitcoin in the future can touch the latest highs will not be strong to survive when the current market price conditions are always declining because they are only chasing the momentary profits from their mining and it is very profitable for the real miners who continue to do mining because if bitcoins are fully or completely mined they will divert their miners to mine another coin according to the algorithm that their mining device has and wait for the coin to rise in price.