How can Elizabeth survive the plot twist?
Needless to say, SPOILERS
"Your" Elizabeth is not present in the drowning scene. If you look closely, she is not wearing the necklace which you gave her at the beginning of the game. I quote here a good explanation which I came across on the 2k forums:
Elizabeth's fate is still rather up in the air. It's possible she exists within the probability space like the Luteces. As far as I understand it:
The first sea of lighthouses you encounter, with all the "stars" (which are really tears) represents the Bioshock multiverse.
From there you enter the Columbia megaverse, a subset of possibilities within the entire multiverse all having to do with Columbia/Elizabeth/Booker.
You enter a final light house where you're drowned by parallel universe Elizabeths.
But Elizabeth never enters that lighthouse with you. The Elizabeth in this lighthouse/universe doesn't have the bruises and scratches from being recaptured by Comstock, and she isn't wearing the bird/cage pendant. Booker even says "wait, you're not, who are you?"
So Elizabeth is still outside, hanging out in the Columbia megaverse. If drowning Booker eliminates the Comstock timelines, this could be visualized as all the lighthouses(universes) containing Comstock popping out of existence in that sea of lighthouses.
Elizabeth doesn't necessarily disappear, because she's shown to be detached from the Bioshock time/space continuum by having the ability to open/enter tears and megaverses at will.The question is, what's she doing now? Sitting around in that endless sea of lighthouses? Knowing the constants and variables of each one? Sounds akin to purgatory. Or even hell. But I guess that's the implication of immortality. Can she visit Booker, and would she even want to? The ending tangentially opens new questions, infinitely, so to speak.
By the end of the game, the Elizabeth with whom we traveled was omniscient and quasi-omnipotent. It seems reasonable to conclude that she was able to remove herself from the Comstock timeline, to survive the erasure of the Columbia universe.
The ending is somewhat ambiguous in this regard:
As each note of the final song is playing, another Elizabeth fades away. The final note is accompanied by the entire screen turning to black - it's possible that at this point the final Elizabeth has disappeared as well. You can watch it here. Obviously - massive spoilers, so no one-boxing :)
However, practically all time travel and inter-dimensional travel science fiction stories have their fair share of issues:
How can Elizabeth even drown her own father before she was born? Doesn't drowning all the possible Booker/Comstocks mean that Elizabeth never existed in the first place? Then, who drowned him? Further, if there are infinitely many worlds, there's not a single one where Booker perhaps never had a daughter? There's a lot of hand waving about "constants" here that they use to get away with it, but it's still a bit silly.
I think that any story which includes these types of elements is highly likely to fall afoul of some type of similar paradoxical situation. (See also: Looper, Doctor Who, Back to the Future, etc)
Warning, spoilers ahead!
I think all answers here are missing a key point, which is (in short): If Booker is never baptized, he never turns into Comstock, so Booker will never give up Anna to Comstock in return to erase his debts. As such, killing the Comstock timeline (by rejecting the baptism) also removes all Elizabeths.
The following graph (source) very clearly explains what happens to the different timelines
