How to reset content from ng-model in a list

I am trying to implement a search which is something similar to this codepen

The problem in this codepen (and for me) is that when I type something it filters correctly, but when I backspace (and delete) what I have typed the list doesn’t go back to being empty - as it was before I started typing the search query.

I have tried resetting $ = {} when the search query length is zero, but that doesn’t work.

Any ideas?