Is there a "soft" fray-check type product available?
 

My DH has a Pendleton shirt with small holes in it - probably caused by cigarette ashes -

Is there a fray-check type product that dries "soft" available to put on the edges of the holes to minimize fraying?

How about ironing on a fusible tricot patch from the inside? it would remain flexible.

Fray Block. I would get it from Amazon in the bottle with a brush for easier application than the tube.

Aleens Fabric Fusion, got it at my local sewing machine store. It is permanent and soft.

Yep. Fray block.

Yes, Alleen's has a product called Stop Fray, it looks a bit like Elmers school glue but does a wonderful job of keeping fabrics from fraying with out there being a hard area where applied. I would think most quilt shops would have it on hand.