Fraying seagrass on stairs

[maltmunro]

Hi. I've got seagrass flooring covering floors and stairs throughout my house but the flooring is now fraying badly on a couple of stairs to the point where its becoming a bit of a hazard. Going to replace the flooring throughout in about a year's time so looking for tips on a way to fix it temporarily. Thinking of using a nail gun to secure the frayed pieces to the stairs - would this work? Thanks.