Does it have to work on mobile touch screens? That has a great deal of impact on practical solutions.
If it has to work on touchscreen, it is likely troublesome either way:
1. User can type in the collapsed control. Problem is then to show the select list, now they have to hit only a tiny target with an arrow button. (Otherwise, they could tap anywhere in the control.)
2. See my previous comment about touch-screen issues if user is allowed to input in the last select list item.
If it has to work on mobile touchscreen, a better solution would be to have an "add" or "new" button next to the control, and use an input in a dialog or else use show/hide to reveal an input.
Alternately, perhaps the last item could be "new", and if it is selected, then you reveal a hidden input or show a dialog.