Unless Made From Fine Fabric
Repairing linens rarely answers for the time and effort involved.
Used to drag out the vintage Elna (Supermatic), or Pfaff sewing machine and spend an afternoon at work when my darning basket got too full, working on linens. However even with a Singer's Flatwork Darning attachment, found results just "eh".
Darned and or otherwise machine repaired sheets always feel rough where the work was done. Handwork is softer, I don't have that kind of free time to spend mucking about darning/mending by hand. *LOL*
One problem one sees in repairing elastic on fitted sheets is opening up the all that hem/casing, inserting new elastic, then closing it all up again. If not done correctly the sheet will not fit properly afterwards.
Back in my nursing related says, before hospitals stocked fitted sheets, we would take the corners of sheets and tie them together under the mattress. Often this was the only solution for constant moving about patient. There simply wasn't another way to keep that bottom sheet tucked for at least a day.