D.M.
Hi L.---I've always taken the worst of the holey jeans and used them as patches for the others. My almost 21 year old still wears patched jeans... not so much in the knees these days, they come that way, but sometimes the back pockets rip at the top, and several pairs have developed holes around the zipper area.
For the bed sheets, they make garters, little elastic straps with clips, just like they used with old fashioned stockings, that you attach to the sheet on each side of the corner. I have one set of sheets, perfectly good/no wear, but the elastic is shot and rides up as you describe. You could probably find those at Walmart. You might have to look online at someplace like Bed, Bath and Beyond.
Good luck! D.