Read the actual lease of the rental you are considering before filling out & paying for a rental application -- the lease should spell out any no-go, early termination, or other penalties or fees. Do NOT assume that all rental agreements are alike or standard. If the agreement only provides for the entire amount of the lease, propose that a one or two month no-go fee be assessed instead, since you have such a short period until your close, & get it added as an Addendum that you both sign. What I'm calling a no-go is where you must terminate in less than a month after moving in. You should have a big enough earnest money deposit connected with your sale to cover a no-go fee. If there is an onerous no-go fee, negotiate it down for your case or find a rental that will.