When I ran contractor's shop, the floor was linoleum covered with
The wire mesh allows any filings that escape the sweeps tray to fall
through so that they don't become impressed into the soles of your
shoes and carried out of the shop.
I think Leonid may not have actual chicken wire in mind but
something more like the steel mesh called hardware cloth.
In Europe, so I've been told, many shop floors are covered with
steel grid panels so sweeps fall through and dropped stones don't go
skittering around. The panels fit between screwed down rails so are
easy to lift up, rather like a reverse dropped ceiling.