Downvoted, unanswered questions have been subject to automatic deletion for a long time. The same is not true of downvoted answers.
On Super User, we have almost ten thousand non-accepted negatively-scored answers posted before the beginning of this year still in existence. Over two thousand of those are scored at -2 or below, having been downvoted by multiple people.
I see no reason to keep these answers around. Based on the votes, they have helped nobody. They're just sitting there, being pointless, borderline-NAA, or otherwise bad. Low quality (but not flag-worthy) posts aren't actively harmful, but don't provide a good image for the site. Additionally, I think people would be a lot more likely to downvote bad things if they knew there was a good chance for the -1 to be refunded in the future if somebody else agreed. (And hey, the poster would get the -2 refunded as well.)
To prevent people from adding single downvotes to cause quick deletion of things they don't like, it would probably be good to require a score of at most -2 before an answer is eligible for auto-deletion. Accepted answers (that aren't self-answers) shouldn't be deleted, since they helped someone. A reasonable time frame for the deletion of -2 answers would be a month after they hit that score; the process would optimally be accelerated by additional downvotes and slowed significantly by any upvotes.
I understand now that some downvoted answers should stick around to show an example of something subtly bad. To prevent those from going away, the presence of numerous comments or somewhat-highly-upvoted comments could be a factor against deletion. I still believe that many downvoted answers are just mediocre/useless and not representative of any common misconception. (See the Super User search linked above.)
Of course, such deletion shouldn't apply to meta sites, where downvotes are overloaded. I think both child metas and Meta Stack Exchange should be excepted from answer auto-deletion.
Otherwise, please make the Community user delete negatively scored answers after a while.