When a user deletes her/his account the questions and answers they posted remain but the username is removed and replaced with user#XYZ. When I put a one of those user 'names' in the site search I get random hits. For example user2110 posted an answer here but when searching for this user name I get 1 result, a question that user posted. Why does the site not show all results, I think being able to do so would be beneficial.
The on-site search doesn't support searching for posts from deleted users, but you can use this SEDE query to find all posts from any user name. Note that that query uses name, not user number, so you have to formulate the parameter as "user####" rather than "####" and (I assume; didn't test) if you search for a name used by more than one user, you'd get all their results. Both of these limitations could be fixed with some edits to that query (but I don't have time to do it right now so I'm just giving a the starting point instead).
SEDE data is updated weekly, on Sunday mornings.