It’s not clear to me if you’re meaning a rug you already have & want cut & bound or rug you want to buy. Assuming the latter, I think that most larger carpet stores, selling broadloom carpet, will / can provide the service of binding a custom size of the carpet. A friend did just that. They couldn’t find the size or design they wanted in a ready made area rug so they bought what’s typically used for wall to wall carpeting. It was at least 12’ wide. They got the length needed & used most of the width They got the color & texture they were looking for. The store cut & bound the rug edges, they bought a pad to go under the rug & done! Looks beautiful. Tape out the finished size you’re wanting just so that’s settled then start visiting carpet stores.