When Morpheus escapes his prison and brings the son of the man who captured him to justice he learns that he wasn´t the target but that his sister Death, was whom they had really wanted to capture. 
When Morpheus learns of this he mentions that they can thank their lucky stars they didn't succeed in their endeavor. 

Do we actually know what would have happened if they had managed to capture and imprison Death? 

Would it have been a little like when Lucifer decided to leave his post and lock up hell or have we at any point been given an answer to what would have happened if Death had been captured?