“i bought some ribba frames years ago and broke the glass in one of them. rather than throw the frame away (or put it aside where it would sit forever while i got round to getting new glass cut for it) i did the following:
removed the mat, leaving just the backing card in place.
bought a packet of home brand wooden clothes pegs, and stained one with the wenge coloured stain i had on hand.
waited for the peg to dry then glued it onto the backing card.