Why don't you take a small piece from the bottom of the top sheet where it tucks in at the foot of the bed and use it to mend the tear? If you do that, be sure to "mend" where you cut away a piece from the bottom or you'll have another mess.

Would just patching it put a stop to the fraying of the "Hole"? Should I sew or zig zag around the outside of it? Would fabric glue be out of the question? In addition to the patch,I mean.

What I would do is this-- Cut a couple of pieces of the sheet(or even another fabric if you want )just a little bigger than the tear. Use a really lightweight bonding stuff like Steam-a- Seam to bond the fabric to the sheet on both sides Then zig-zag all around the edges a couple of times and then zig-zag back and forth and up and down to really make sure the patch is well fastened down. Sheets take a lot of wear and washing so you want to be sure it is well mended. Good luck. Hope this helps.

Thanks, everybody, I will do this.