Does Stack Exchange policy discourage deleting your own answer after downvotes/criticism is received?

You can get a badge by deleting your own answer with score -3 or lower. While some badges promote behaviour which is questionable in some circumstances, I don't think this is the case here.

If a user posts and deletes multiple answers with negative score, they'll eventually run into an answer ban, so any risk of 'abuse' is minimal. And in exceptional cases, moderators can have a private word.

I self-delete answers on occasion when there seems to be little point in keeping it:

• if there's another, better answer than mine and I feel as though my answer detracts away from that
• if I drastically misunderstand the OP or the OP changes their question so that it no longer applies to my answer to such an extent that it's not really helping
• sometimes my answers might get comment-stormed from people who don't share my opinion, so I just shrug and delete the answer because it's obviously not productive

There's no site-wide policy on self-deleting and how to deal with it, on the whole the site isn't beset with this issue.

Any localized toxicity should be raised with site moderators or posted on the relevant meta for discussion.

There's no real formal rule against it, but good reasons to discourage that. A good user's mindful of their posts - posts not for the sake of posting or the off chance of getting upvotes or other reasons, this fills the site with... less useful content.

So there's two possibilities here. A lower reputation user gets post banned, and.. is confused what they did wrong cause no one tried to tell them. Or a high reputation user who can't be post banned goes for volume, cause there's no downside to deleting a downvoted question, or one that's obviously incorrect.

Both of these are bad for us. We either lose a new user we could have educated (and maybe we need better ways to do this), or we have a high rep user who's not acting in the best interests of anything but accumulating reputation, and skipping out on the bad sides of poor quality posting. We don't catch everything so it might also encourage others to do it if there's no critique or votes. We also might get accused of targeting a user if they're constantly getting posts deleted, even if its warranted.

I'd say its toxic in terms of the mindset and what it can do to the site.

Practically we treat it as we would treat low quality content, mass vandalism, or any other appropriate guidelines that fit.

You ask specifically for policy, but I'm going to approach this from a more systemic standpoint, particularly concerning downvotes– based on how the site works, no, it's not broadly discouraged, and would fall more into a site norms area. If anything, I'd argue that current site design actively encourages this behavior through its incentive structures.

As it stands:

• We have the bronze Peer Pressure badge, which directly rewards this behavior (as long as the score is -3 or below), as @Glorfindel mentioned already
• Self-deleting a recent, negatively-scored post restores your lost reputation

Particularly with the latter, just from an incentives standpoint it seems crystal clear why people would want to do this: they tangibly benefit! The more critical the voting feedback, the more reason to wipe the slate clean.

But zooming out a bit, if we view the goal of Stack Exchange sites as "building a library" (or many), then if I post something in earnest that other users signal as a bad contribution, then self-removal arguably isn't just sensical for me, but actively beneficial to the library! I don't think it's unreasonable to assert that we don't benefit from "bad" answers, in the general sense.

Given, I'd also say that fixing is superior to self-censorship. But depending on the site and the context, that may range from easy to downright impossible, especially on sites scoped to a less objective subject matter than, say, programming, or if my answer turns out to be just incorrect.

In practice, there's nuance here, and things are downvoted and deleted for a myriad of reasons– I'm not privy to the specific case referenced in the question that produced the quoted comment, and I can definitely imagine a hypothetical where a user deletes their own post in the midst of otherwise acting poorly.

But overall, I just find it really difficult to see this as a bad behavior when I look at how the site currently functions and rewards users; much less call it "toxic" for a user to remove something that the community around them has explicitly signaled as poor, low quality, and/ or low utility.

With no apparent incentives or guidance to the contrary, it feels like a humongous ask to expect anyone, old or new, high or low rep, to want to weather downvotes when they're given little to no reason to do so.

It's a valid caveat, however, that "negatively received" may not necessarily equate to "negatively scored". If, for example, a user is unable to take genuine, constructive criticism, or they rollback helpful edits, or delete their post after meaningful refinement by the community– that feels more legitimately classifiable as "toxic" to me. Collaboration is the name of the game here; it's woven into the DNA of SE sites, and it's not something a user can opt-out of.

Some other thoughts that came to mind that didn't weave well into the above:

• The asymmetric reputation impact of votes (+10/-2), I think, does reward salvaging answers over deleting them, since it only takes a single upvote to nullify the reputation impact of five downvotes
• I'm definitely not saying that the current design can't or doesn't necessarily have negative side/ knock-on effects
• Whether site design should be this way, or whether it could be better if tweaked to some degree, is a worthwhile, but separate, discussion

This post is an expansion of a comment I made under @JourneymanGeek's answer.

I've seen comments on Super User Meta where users call it "toxic" or "bad behavior" to post an answer, and then delete it when it receives negative feedback or downvotes.

Since we are talking about my comment. I find it extremely annoying to spend 5 minutes of research, and subsequently submit feedback to a user who submitted a factual inaccurate answer, only to find it instantly deleted the moment the feedback was provided while simultaneously constantly complaining about the downvotes they received to past answers without receiving that very feedback that was provided which ended up causing their answer to be instantly deleted.

So I absolutely find the behavior i just described extremely toxic. I am not talking about the rare case of as a question answerer, not understanding that rare question, and completely missing the mark with an answer. I am talking about deleting any answer that receives any negative feedback or downvotes, nearly instantly, consistently (as example at least once a day).

What I describe absolutely is routine with an extremely small subset of users, and they have to date, never been impacted by an answer ban because of the thousands of answers that they submitted.

I have a problem if I spend time researching a topic before submitting an answer or researching if an answer that was already submitted is actually accurate, only to find that contribution that was “deemed good enough to submit” being deleted, once any negative feedback is provided publicly. It shows me that perhaps the negative feedback is not worth sharing, if it means, the contribution will simply be deleted after a single comment.

Heck, what do I know, I am only human.

Deleting a negatively received answer is by no means "toxic" behavior, by any definition of the word "toxic". It is usually a good thing, because most of the time downvoted answers are wrong, and the goal of the Stack Exchange network is to become a repository of knowledge (of true, high-quality knowledge, of course).

Some argue that deleting own downvoted posts unfairly avoids loss of reputation. But in this case, that is a good thing because it removes wrong or low-quality content from the site. In any case, calling it "toxic" is really a stretch.

Deleting poorly received questions is a different thing, because someone may have spent effort answering it and that answer will also get deleted with the question. But the site does not lose anything of value if a low-quality answer is deleted by its poster.