I've played bass for 40 years, acoustic bass for 30, and have done a good bit of the repair work on various basses I've had. When a crack starts, and taking the top of the instrument off is not done for repair with a cleat, the use of fabric is viable.
A fabric patch repair is done by taking raw linen and impregnating it with hide glue, applying it across the crack, and squeezing out the excess glue. Once it's dry, the repair prevents the crack from widening. The canvas acts like a staple, but over a large surface area.
This is probably not a new idea, but I think this might be viable for strengthening those ultra-thin vertical surfaces found in sidelock inletting.
How tight the inletting-to-action fit is would have to be a consideration, and how thin the material is would as well. Bed sheet material would be quite thin, with a lot of fibers. Hide glue would not be the choice in this application, but some other super-thin adhesive, such as water-thin superglue.
Just some thoughts. I think it might work, and I plan on trying it as part of an unfortunate stock head repair I am facing.