I spent a lot of money on a thick memory foam topper and cover only to have both start falling apart. The cotton zippered topper that came with the foam just disintegrated. It's still on my topper but hanging by threads, but still worth leaving on for the little protection it gives because the exposed memory foam starts to split if you move around on it... which is why toppers are a must.
Anyway, I bought the Comfort Memories topper to cover both the old frayed cover and the memory foam. It somehow holds everything together and looks nice, too!. Zero issues with tearing. The ONLY complaint that I have is that it's not a zipper cover, which is my fault for not realizing when I bought it. It only covers one side of the foam. Still does the job for me, and I plan on purchasing a second.... hoping they have a zippered version of this on.