Every offer has a non-compete agreement as part of the purchase agreement.
The non-compete will specify that the owner/seller cannot compete with the buyer for typically 5 years within a specified distance or sometimes counties. The non-compete may include family members if they have been involved in the business.
For manufacturing businesses the non-compete distance may be the entire United States if their customer base is nationwide. For service businesses the non-compete distance is typically the service area the company has been covering.