I'm not sure if anyone has filed this bug yet, but I can't find it on here. So
I searched for a user on the user page, then cleared that text box. Now the next/previous buttons are gone.
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This is intentional? Clearing the text box blowing away the buttons? I find that hard to believe. I replicated it -- it feels buggy to me, too.
Regarding the dupe:
This really isn't a dupe, it's more an elaboration on the question random linked. The question linked describes the behavior, and the fix was to remove paging when the input box is used. While I still think that is even buggy, I can understand it.
However, once the input box is cleared, as per this question, then the original behavior should be restored. After all, all you've done at that point is undo your original actions. At that point, it should be as if you never performed those actions -- but it's not. And therein is the bug.
If you're filing as a bug, it's status-bydesign.
However, if you were to edit your question as wanting it to behave like you want it to, that's another thing entirely.
It would be good to see the pagination stick around if you're searching for a particular whathaveyou in the DisplayName.
SELECT concat('<a href="https://stackoverflow.com/users/', Id, '">', DisplayName, '</a>') as author, Reputation FROM users WHERE DisplayName LIKE '%cthulu%' ORDER BY DisplayName ASC
Pretty linking ripped from Shog9.