When a question is deleted, any questions that are closed as a duplicate of that question should also be deleted. This should be a rule at least on regular sites. Meta sites could be a little different, since duplicates on metas may not be exact duplicates, but problems arising from that will constitute such an edge case that they're probably not worth handling specially.
This post originally asked what to do with questions closed as duplicates of deleted questions, but I found "Duplicate of...[deleted post]" almost immediately after asking, so I have reworked it to request the feature Shog9 suggested in an answer there.