When a company is acquired, how about its patents?

Your question omits two crucial facts.  1, is Company B an independent legal entity, such as a corporation or limited liability company?  Since you're writing about companies acquiring or being acquired, I will assume yes.  The second question is then whether Company A acquired the equity of Company B, i.e. (if B was a corporation) acquired the shares of Company B stock thereby becoming the new owner of Company B?  Or did it acquire the assets of Company B, i.e. buying the inventory, leases, intellectual property, goodwill, etc.  Of course, transactions like this can be structured in many different ways to accomplish the results which the participants want, including structures which are part equity sales and part assets sales, but in general if Company A acquires Company B's stock, Company  B remains the owner of all of its prior assets, including patents, and remains liable on all of its obligations, including employment contracts, it is just that Compnay A, as the new owner of Company B, will feel the economic impact of these transactions instead of the prior owners of Company B.  If Company A just acquires the assets of Company B generally would not be responsible for Company B's obligations, and whether it would now own Company B's patents, or Compnay  B's employment contracts (to be responsible for the obligations thereunder) would depend on whether those assets were included in the sale..