There are several options for finishing carpet remnants or pieces of broadloom carpet to make area rugs, including binding, serging, and fringing.
Rug Binding — Area Rug Factory
Make a Rug From Leftover Carpet : 3 Steps (with Pictures) - Instructables
3 Options for Stitching Carpet Edges to Make a Rug
3 Options for Stitching Carpet Edges to Make a Rug
The Best Alternative to Expensive Carpets: Binding a Carpet
Rug Maker - Bespoke Rug Edgings - Jacaranda Carpets & Rugs
Rug Binding — Area Rug Factory
Carpet - Wikipedia
8-Sewing band on the carpet side to prevent edges rolling and stabilizing
How to Make a Jelly Roll Rug - Create Whimsy
Everything I Learned About Stair Carpet Runners And What We Ended Up Installing (Including What It Cost) - Emily Henderson
The Best Alternative to Expensive Carpets: Binding a Carpet