Anywhoo ~ Gents Braces, trouser supporting for the use of, are not easy to find these days. John Lewis and a few decent gents outfitters seem to stock them but their popularity has diminished over the years. I always use them to ensure a decent "hang" to a suit. I have 5 pairs in different colours to blend with ties/suit combo but I confess I seldom wear a suit and never a tie these days.
I suspect the reason you get asked for them is that the are damned expensive items but by the same token that would be the reason you don't get many pairs handed in. Those who wear them tend to hang onto them until they're are truly knackered.