This situation is this: your home is for sale and the prospective buyer wants to buy it, but says, “I like it, I want it. But I will not have the money for a couple of months. Can I move in until we finalize the sale?”
Possession of a home usually changes from seller to buyer at “closing,” but in some cases a home buyer will ask the seller to grant possession before closing. Sellers make the final decision as to whether an early buyer possession makes sense, but you will find the seller’s agents RARELY encourage this situation. Too many things can go wrong.
One of the best ways to kill a sale is to allow a prospective buyer to move in a considerable time before settlement. Often when this occurs, it is difficult to get the buyer to go to settlement. He may keep findings things wrong with the house, keep insisting they be fixed, or even worse demand that an adjustment be made to the price. Can you imagine if the loan never gets approved and the buyer now is living in your home? What if he trashes the house or makes unwanted changes?
Sometimes the result is even more disastrous. The seller becomes disgusted with all the alleged complaints and calls the whole sale off. Now you need to get the buyer out of the house, potentially do some cleaning, repairs and ultimately the seller must then start all over again! 
In my opinion, it is better to let a house sit empty than to let a prospective buyer move in before the closing date. Although it is not good for a house to sit empty for a long time, it is still faster and a better way of selling it with the least amount of trouble. If you do agree to early buyer possession, it should most definitely be handled with a written agreement that describes the duties any responsibilities of both parties. Protect yourself and your investment.