A dead short to ground should leave you with no brakes and a blown fuse, though if only one wheel is getting power on the blue wire it's possible it could be locking only that wheel up. Also, if that one problem wheel has a short in the electromagnet lowering it's resistance it's possible that most or all of the current is going to that one wheel only too.
Brake controllers also all send a "phantom voltage" on the blue wire so they know when a trailer is attached, though I don't know if the current is enough to cause a problem if there's a problem with one of the electromagnets. Probably a little different with each model.