Lining a run

At the moment the run that's attached to the rabbits playhouse is on paving stones, I am looking at having half on the paving and half on grass as I am extending it but am worried about them digging out while I am at work.
The garden is secure and they have the run of that whie I am home and they have never dug so far but better to be safe.

Is there anything I can use to line the bottom of the run to stop the digging? Like some sort of soft mesh, I don't want normal mesh in case it hurts their feet, but it would need to be strong in case they chew a hole and then dig.

Part our garden we lined with bricks about a foot under the turf so the rabbits could dig but only so far. But with the portable runs we've attached chicken wire to the bottom so they can't dig out. Providing the grass is nice and long then you don't notice it and we haven't had any problems with the bunnies feet.