I'm a moderator on one of the beta sites, and we (the moderators) wind up deleting a large number of answers from new users who don't understand the platform.
Many of them treat answers as comment fields (since users with 1 reputation cannot use actual comments on other people's questions), or post what should really be new questions as answers to questions they feel are related.
Some answers also get deleted for simply not meeting basic quality standards.
For these deleted answers, we provide a standard comment to welcome the users, and provide a little bit of guidance for getting used to the site. One of the outcomes we'd like to encourage with this stock comment is for the new user to edit their answer to improve it.
I know some other sites, such as skeptics.se, frequently delete non-answers, and request improvements through edits.
However, if the new user does follow through, and makes the edit, it is extremely easy for a moderator to miss that, unless the user is savvy enough to flag it for moderator attention. We've experimented with asking users to flag for moderator follow-up once they provide additional information, but adding that additional step to the process may further discourage a new user (our subject matter attracts a larger group of non-technically savvy users than many of the other SE sites).
If there was some sort of automatic notification when a user made an edit to a deleted answer, so that moderators could check and see if the user improved it to the point where it met community standards, it would help us to encourage and retain these new users.
My first thought would be an automatic flag for moderator attention, but I could see how that might be a problem for graduated sites that already have a high volume of flags (ours are few and far between). Perhaps automatic flagging might be something that each site can opt in to or out of. Adding this to the review queue, or perhaps a notification in the inbox of the moderator who deleted the answer, are other possible methods that might work.