[Spellman]

If a group is dead, it will be automatically captured at the end of the game.

So, in this case, the black stone is auto-captured, and you get the territory within as well.

So, yes, playing white stones to capture is actually detrimental to yourself. But also imagine if black keeps playing. They would be giving away free captures since black can never create eyes. And once the space is almost filled white can play 1 stone to capture all of the black stones.

Edit: Another way to imagine it is if neither player could pass. While yes White would lose territory as it played stones, it would be compensated by Black playing stones that will be captured in the end. Thus it becomes a wash, and thus why dead groups are auto-captured.