My sneakers often wear out in the lining, especially at the heel, before the rest of the shoe. So, I mend the inside of the back of the heels with either clear First Aid tape - or white First aid tape (which matches my white sneakers).
If the padding has totally worn through at the heel, you can also replace the worn padded lining with a piece of molefoam and glue it or tape the edges. You may have to keep after the tape, as it slips after a while, but it makes your sneakers wearable and comfortable, so you can get your full use out of them.
I have patched the inside heel area of sneakers by cutting a piece of fabric to fit the area and use Tacky Glue on the fabric and press in place and let dry thoroughly. Sure extends the life of the shoes!
I think it is the socks that get nubbies on the heel that acts like sandpaper on the shoe lining.