Don't hate this is a Theory. I cant get over the end of Burial at Sea part 2 so here is what i tell myself to get over it.
I think i may have put this all together were i feel alot of good closure in this ending. Spoilers of Course:
I think this Elizabeth is from another universe that was connected to Infinites. In the beginning Liz was talking about how the first time she was in contact with rapture was when the OTHER Booker and Elizabeth got there. At the end of infinite Booker had his normal life and you know that Anna was in the crib that ONE universe the Bioshock Infinite Universe was over and had a good ending. But now that that Universe is done. The other Universe with the Noir Elizabeth with the Constants and Variables is an Altered version of Infinite. To kill Combstock "Detective Booker" and to save her Universe like all of the other sea of doors there trying to stop the events from happening in different universes. But when the Luteces came back at the ending of BAS part 1 they told her to go with her. One universe went with them and that was the end of that problem they killed combstock. The other universe has her want to go back or stay and in a result she gets killed by the Big Daddy the Luteces then give the dead Elizabeth another chance but the consequence was you will be Normal like everyone else. Like the twins said "I cant believe THIS ONE gave up the reality of Paris to go save a girl she doesn't know." Elizabeth has done her quota and Killed Combstock in this Universe. So if she requests to go back and save sally sure knock yourself out but you can die. She knew that she wasn't going to make it out of there alive when she remembered what she had requested to do when she saw herself dead there in the beginning. This is version of Elizabeth is Rapture Elizabeth no quota from the other realities to kill combstock this is of her own decision to save sally. She did die in the end and its horrible to think of but this is one of the many realities, not the one from infinite. Pretty sure Christopher Dunn had a similar concept. Great game couldn't ask for a better one i just hope 2K doesn't ram the franchise in the ground which you never know they may have learned there lesson either way i loved Bioshock 2 not as much as 1 or Infinite but it was good in my opinion.