What can I do to lift or reduce a suspension? contains good advice for appealing manually-imposed moderator suspensions, which always have a moderator message attached to them that the user can reply to.
However, this FAQ doesn't address how to appeal the automatic 14-day suspension imposed when a moderator deletes or destroys the account for spam or user conduct. This automatic suspension doesn't carry a moderator message with it, and so there's no way to contact the site's moderators and appeal it as per the above FAQ.
That FAQ does also mention contacting the team, but the team has often in the past simply closed appeals of short suspensions without action, as they know that by the time it makes it through their backlog it's usually already expired, so that may not be a useful option. (This action doesn't make sense if the author has made posts, in which case they won't be associated with their account anymore and should be re-associated to their new account if the deletion was indeed invalid, but I imagine this may be often overlooked.)
How is one supposed to appeal the suspension that is imposed when their account is deleted using one of the above options, or the removal of their account in such a manner? (They can't post on the per-site meta, and so such users often come here, where their questions are generally marked off-topic as site-specific.)