It's a hack fix, but sometimes you can tuck the cloth back in, and maybe wedge a sliver of a playing card along the backside of the featherstrip.
The proper way, would be to pull the rail and recover it. You'll need to shim your featherstrip, to get it to fit snug. You can use masking tape. Some guys even go the extra step, and use glue (3m77 or even just a glue stick) on the featherstrips.