I don't know how you would find a spot to accommodate this.
Maybe someone from a residency program dropped out, one the OP wants to go to, and they are trying to set up a way to enter part way through the year?
I literally cannot think of another reason why someone would both want to leave their current program and go to a different program somewhere and plan for it to be mid-year.
It is not mid year. It's end of June... the time to arrange and transfer right now (Apr-Jun typically).
As mentioned, find an unfilled spot as quick as possible and make it happen.
Be aware that most programs available are probably as terrible as the one you're looking to get out of... but check CASPR list and call around.