Don't waste your time on trying to fix the paper. You'll spend way more time and trouble trying to make it look right and it will look just like what you are doing (too cheap to do it right). And you'll have to do the wall the right way AND then have to do the closet, too! Chances of getting a full strip off, intact, and with the paper backing is slim to none. With out the paper backing, repasting just the front (printed) paper will look horrible. You won't be able to get it smooth.
You are trying to sell a house in a buyers market. You should do what you can to make your house appealing. Don't do a "make do" patch work of fixes. Do it right the first time. Strip the old paper off, wash the walls to remove the old paste, and spend the $20 on paint.