I just answered this question. The name of the user who asked the question is gray, so I assume he/she is removed. Now what? Is anybody able to accept my answer (assuming it is correct for the moment, I'm just asking out of curiosity) instead of the OP? Or has this question to remain unanswered until SO stops working?
You'll have a warm fuzzy feeling that you helped future visitors with the same question.
You may get upvotes, but no one will ever be able to mark your answer as accepted, no. The question will, forever more, remain without an accepted answer. Until the heat death of the universe, or the demise of Stack Overflow, whichever comes first, of course.
Note that the user can appear grayed out because the post was migrated from another site and the poster does not yet have an account on the target SE site. When the original owner does create an account and associates it with the source site account, ownership will automatically be fixed and the OP can still accept your answer. For your specific case though, the owner is indeed deleted.
The user will not be able to accept your answer, on account of the user ceasing to be. However, other users can still upvote your answer to indicate that it is a useful answer.
It's not technically "unanswered", though, so long as your answer is useful and solves the problem. It may not have the green checkmark, but the important thing for the post itself is the presence of a solution, not the checkmark.