In Bioshock after killing Big Daddy I can't find the Little Sister he was protecting. Is it possible she was killed, or one of the NPC got her?
No, but it is possible the Big Daddy wasn't protecting any Little Sister.
Big Daddies roam Rapture and get Little Sisters from the vents, but you can kill them before they are protecting any of them.
If he was protecting one, she should stay near the deceased Big Daddy, they cannot die nor be taken by any other character.
Try following the big daddy around for a bit before attacking him. In the first BioShock, he'll eventually go up to a vent and pound on the wall. If a Little Sister climbs out, you're in luck! If not, then don't bother killing him: Not all Big Daddies escort Little Sisters (These are the ones you should hypnotize to help you!). However, if you kill a Big Daddy before he helps his Little Sister out of the vent, then as far as I can tell, there's no way to get her to come out, save from leaving the area, and returning.
Also, I'm not sure about BioShock 2, but in the first game, if you pause, some icons appear at the bottom of the screen indicating how many total Little Sisters are in that area. They also indicate whether or not they've been rescued/harvested, or are still with a Big Daddy.
In general, Little Sisters cannot be taken by anyone other than you. However, If you do kill a Big Daddy and the Little Sister is nowhere to be seen, chances are good that she was recently helped into a vent by the Big Daddy you just killed. If you wait around for a while, another Big Daddy will come and get her. Big Daddy's will only respawn if you failed to aquire the Little Sister he was partnered with. On a side note, In the part where you're roaming around the Upper Wharf early on after talking to the crazy fisherman guy, all three Big Daddies will show up in the same room if you wait around enough. And, it's near enough to a Vita Chamber that you can keep wearing them down until all three are dead.
Alright, so I'm playing the game literally as I type this, and I know for an absolute fact that there are rogue Big Daddies. I'm watching a fourth Big Daddy walk past the dead body of a fifth and pound on a vent right now after I (saved) all three Little Sisters on the level. He never found a little sister, so I just took control of him and brought him back to the room where the three I had killed previously and saw yet a sixth Big Daddy!
I've chased after Little Sisters after killing their Big Daddy, and watched them climb into one of those holes in the walls. After this happens, you have to leave the area and come back after a new Big Daddy shows up. Kill the new Big Daddy, and nab the Little Sister before she runs away.
@Keaanu is wrong in his answer. In Bioshock 2, if you have a little sister that you have already adopted. You can't harvest/adopt another one.
I accidentally killed a big daddy with a little sister, and I can't pick her up. So, eventually I left to gather enough adam for her.
After that I chased another one to get the last little sister, I saw him banging on the hole. No little sister. :( Then I remembered that I left one of them behind. So, I went back to that area. To hear a little sister crying. And I adopted her.
Hope this helps someone.
Check the options screen to make sure there are still Little Sisters in the area. If you are close to a vent, a Little Sister may crawl back in before/after you battle the Big Daddy. You will often hear her say "I'm tired. Time for beddy bye". If so, move between the Little Sister and the vent before you take on the Big Daddy. I found the best time is when the Big Daddy is either fighting another foe, or the Little Sister is retrieving Adam from a body. If you use "hypnotize Big Daddy" on a Big Daddy guarding a Little Sister, she will return to the nearest vent. Rather than kill the Big Daddy, just let it go to retrieve the Little Sister again.