Not for a staysail - a brayle is a way to draw in a sail by pulling on a rope which goes over a pulley fixed onto a spar of some kind. By definition, a staysail has no spar.

You could clew up a staysail by drawing the clew of the sail up the stay so that the leading edge is all concertina-ed and then folding it up and tying it so the fixings could then be released and the sail lowered or carried down the mast/rigging. That might be safer than trying to wrestle the sail downwards and move it back along the bowsprit.

It still makes no sense, though.