Should the answer that answered the original question be:
- Added to (leave both answer)
- Deleted (and create another answer)
- Have two answers
I would say rewritten. That way the answer matches and you have the the edit history.
Adding to the answer might be ok in cases where the original answer still have value.
Deleting the old answer hides most of the history so this is a poor choice.
Two answers is just wrong.
Usually the best way is probably to rewrite the answer, as it is no longer a correct answer and also bound to get downvotes (unfairly, but what are you going to do.)
I would say this largely depends on the case.
If the original question was a good enough question on its own, but the changed question is different enough that the answers are significantly different, then perhaps the changed question should be posted as a separate question entirely instead.
Otherwise, the answer should be carefully rewritten so that it correctly addresses the current question while still including data applicable to the original if this is at all possible.
In the end, the goal here is to not lose information while still making sure the Q&A structure is properly intact.