It's a pretty tune, Guest. If you don't get it identified, you have two choices - let it die, or compose a new ending for it.

First, repeat what you have, changing the second half of the repeat slightly. That will do for the A part.

Then hum a B part in your head. I suggest you start with a G chord. I call that "turning the corner" - switching the modality at the beginning of B. Get back to Em by the end.