If a company files for Chapter 11 and then exits Chapter 11 because it gets purchased by a different company

My colleagues have provided good answers to your question. I also suggest that you talk with a bankruptcy attorney experienced with chapter 11 issues for further details on how you can proceed or otherwise deal with the outstanding debt.

Absent an order relieving the creditor from the stay, a lawsuit based on a cause of action that arose prior to the filing of a bankruptcy including a chapter 11 , if filed after the filing of the chapter 11, would be in violation of the bankruptcy stay. If filed before the bankruptcy filing it would be stayed, and dealt with through the chapter 11. In either even the claim of the person filing the lawsuit would have to be dealt with in the chapter 11 case. The dismissal or other resolution would depend on on the chapter 11 plan. That would need to be discussed by the debtor and debtor's counsel.

“During the Chapter 11” implies that the creditor violated the automatic stay (the action is void) unless given permission by the bankruptcy court. This sometimes happens when a creditor needs to liquidate the amount of its claim in another court. The corporate form of the debtor matters - if it is an individual with a DBA the suit could not ordinarily be brought against the new owner. Regardless of corporate form, if the Chapter 11 plan does not provide for assumption or satisfaction of all liability of the former debtor, the post petition claim would not lie against the reorganized debtor. Even if the new company has the same name and is healthy.