Ideally, closing of work object results in lost of data. Pega closes with warning that data could be lost. It will be logical confusing, if a user wants to discard the work object changes and it would compel it to satisfy all the validations on the screen and then going ahead with closure.
Closing a work object is usually performed, when user is done with the process and intends to not work on the work object further. Thus, it won't be a good design implementation as per my knowledge.
Though, Could you share your use case, as why you want to validate a work object on closure with detailed explanation?
When you say "close" do you mean "resolve" or "close the window/tab in which the item is open"? If it's the former, I assume all regular validation would be applicable. If it's the latter, I agree with Asif that it raises some questions about potentially being confusing for users. You should be able to trace whatever is called on "close" and presumably add standard validation in there. If it's final, you might need to put your validation into a wrapper activity. All of this still doesn't account for a user literally closing the browser. In that case, you are pretty much out of luck.