Usually a flange as it flaps. But you can place a very narrow border in a quilt either in the binding ie flange flap or between sections.
I put flanges by my borders but find it easier to cut 1" strip fold. In half and put around edge and then bind in normal way. I find I am not capable of stitching exactly on the right place and machine line, flange anD binding always looks a mess. The way I do it no problem. I have wondered if you could cheat with a narrow border by using sticky celtic knot binding and sewing that where ever you want.