How can I create a taxonomy meta-box with search suggestions but no new terms input?

Question

I was wondering how I could setup a taxonomy metabox on a post edit page that would be similar to the "tags" kind (with search field and automatic suggestions), but without the right to add a new term.

So for example if I'm typign a word, I get suggestions of terms that I can use from the existing terms list, but if I type a word that doesn't exist, then it doesn't add the terms to the list.

EDIT

Actually, what I'm looking for is exactly the behavior of the "Search" functionality in the Menu Editor :

As this is a core WP behavior, is there a way to use it on post edit pages too ? I'm wondering because these blocks look exactly the same, both have the "view all" and "most recent" tabs, but "search" is only present in the Menu Editor.