I have never seen this done. I doubt the wicker is strong enough to stretch the fabric on tight enough..then tack or staple in... You can certainly make the cushions to lay in the seat, put in back of seat... One thought may be to check your county/area and see if there are any sheltered work shops. There are work shops where people with dissabilities are trained in kaning... (hmm or is it caining)? It's what you called reweaving. ;o) That is expensive, even in a sheltered work shop...and it can take some weeks to get it back... They do like getting in the work so they can teach and produce a usable product.

OF course depending on where you are going to use it...You can try using a heavier cord, (twill) to sort of reweave it (pull it) back together yourself to make it sturdier... Cushions in the seat and back could cover the work... and you can likely buy the cushions reasonable at Walmart K-mart... BedBathandBeyone, or my favorite Pier One Imports... they have the nicest and more different things... ;o)

If the chair is going to sit where it is easily seen from the back... and that "self pulling it together" would show... not a good idea...