> These things have kill switches built-in, don't they?
Not all of them have kill switches - Knight Trading had something with no kill switch that cost them $400M in a matter of hours. (It wasn't even a trading program - some kind of simulation system that was erroneously allowed on the real market).
You could say "it didn't need a kill switch, because it wasn't a trading algo!". But many trading systems are made of small parts that can break, and you only know your kill switch works after it saved you - otherwise, it's just an "untested feature before QA".
> My question would be, what happens to the markets if there is a quick fall, the algorithms shut down, and all the HFT liquidity is removed?
We've seen such mini events before. We see what's known as a "flash crash" (price goes down significantly within seconds, only to come back to more or less the same place), or alternately, a "flash smash" if it goes up (to come down later). This has been happening since 2007 at a frequency of about once every two months. Sometimes trades happening during the flash {sm,cr}ash get retroactively canceled, and sometimes they do not.