Desktop mats or tripod base mats can be asbestos cement or less often asbestos millboard. The softer millboard type didn’t last to long as they were just too soft and also absorbed any spilled liquids. But labs still often have asbestos cement ones in use or tucked away in a corner somewhere.
The hardier mats can last decades in a lab slowly shedding asbestos with each use or when collected or thrown into a cupboard. Also like the gauze mats this source of asbestos fibres can end up being in the resipirable zone of the user.