Without looking for a foreclosure, how could an investor buy-back the piece of real estate that he just sold, at a better price? Is it possible? After the closing of the deal what possibilities are there for the person to buy back that property, is there a common process to do this? What are some options to do this, if it is even possible?

You can only buy what is for sale. If the owner(not you) wants to sell it back it's up to him. If he doesn't then SOL.

It's totally up to the new owner. If he agrees to sell it back, you can buy it. If not, too bad.

Contact the current owner and make him/her an offer to purchase. If he/she accepts the offer, you have a deal.