If you search amazon for "plastic repair kit" they sell this thing (20-30 bucks) that looks like a soldering iron. They heat up little metal staples and you can sink them in from the back. Just make sure all glue is cleaned off, and practice on some similar plastic to see how long you need to heat the staples for. I had an ice box with the same issue and did fix it, but then replaced it with a 3 way
fridge, I made a video on YT about the install.
(edit, my crappy spelling)