Something that you might have noticed when you played capture go is that you can't take up your own final liberty. This would leave your own stone with no liberties, so it would be suicide, and you would lose. For example, if a white stone is played at the marked location then it will die:
One exception to this is that sometimes both you and your opponent run out of liberties together. When this happens, the player who just moved wins; the opponent's stones are captured. Here is an example:
Here is another example that shows up fairly often in real games: