You are allowed to throw from a destructor as long as there's not already an active exception unwinding the stack. In my experience this is a total non-issue for any real-world scenario. Propagating errors from the happy path matters more than situations where you're already dealing with a live exception.

For example: you can't write to a file because of an I/O error, and when throwing that exception you find that you can't close the file either. What are you going to do about that other than possibly log the issue in the destructor? Wait and try again until it can be closed?

If you really must force Java semantics into it with chains of exception causes (as if anybody handled those gracefully, ever) then you can. Get the current exception and store a reference to the new one inside the first one. But I would much rather use exceptions as little as possible.