I think to do it properly you need to "roof" the entire area with chain link. Some dog kennels come like that, with the same stuff on the top. No doubt this would also be expensive and might require supports mid run. How big is the area? The chain link would also have to be fastened along the sides very securely.
I know dogs that can climb and 8 foot high fencing might not be enough either. But some dogs seem to be able to get out of anything. Mesh fabric, it that's what you meant, no way, too easy to rip with sharp claws and strong teeth.