I dont know how the do it at other places, but here in indy you dont have to bring a partner. If there is an odd number typically the better player on the first team that is eliminated plays w/ the odd man out, and they just work the bracket out so it still an even and fair flow to allow for this, its normally not even noticed by many unless you are the odd man out, or the one who gets the new partner.
again, this is just how we do it here, i dont know if thats standard or not.