Yes it is possible. It is really up to the new buyer. Like what was said below, it requires a "post possession agreement". I don't recommend this, however. After close of escrow, the home really belongs to the new buyer. There are many things to condsider, including legalities. Really, the risk is too great for just one more day. I would tell your mom to do anything she can do to move before the close of escrow.
The standard time period for a seller to vacate the home after closing is immediately. In order for the buyer to conduct a thorough walk-through of the property prior to closing , all of the seller's possessions must be out of the home and it should be in move-in condition for the new buyer.
That having been said, if you are going to require an additional day after the closing this should be negotiated and arranged at the time of your purchase and sale agreement. This is when it pays to have a good real estate attorney to set this up for you. There is also a matter of liability for that additional day since your mother will no longer be the owner but would be responsible if anything happens to the home while she is there.
It would be a much better solution just to plan the closing one day later if that is possible.
Speak with your mother's agent as soon as possible to let all parties know about your mother's wishes. Have the agent clarify what the contract stipulates. From my experience, these kinds of accommodations can be made if you show the buyer some consideration.
Congratulations on the sale.
I would really think the best thing would be for her to have all of her stuff packed away and when closing day comes she takes a shower, locks the door and rents for a day if necessary. If the problem is moving stuff out, you could ask (in the contract) for one day to remove her stuff. Buyers may agree or not.
For a smoother transaction rent a storage unit for a month. It saves a lot of hassles. She can always pack a suitcase in 5 minutes for any personal items remaining.