Whoever bought the business will probably send out W-2s for the old business. They have until January 31 to mail them, and it would take a few days for the mail to get to you. So wait a couple of weeks to see if you get a W-2 before you assume that you're not getting one.
You could also contact the purchaser of the business and ask them what they are doing about W-2s for employees of the old business.
