Can a company enforce contracts through the purchase of another company?

Most contracts (other than those for personal services) are freely assignable, absent language to the contrary in the agreement.  Thus, if you contract with Beyonce to appear at your wedding, she can't assign that personal services contract to Rihanna, but if you contract with a soda provider to provide 50 bottles of assorted soft drinks, that provider probably can assign the contract to another beverage business.  Assuming your contract was validly assigned, you would have the same rights in your dealings with the assignee as you previously had in your dealings with the assignor.