We saw this as early as Hurricane Allen in '80 when just a fraction of the cotton was modules, most was still in trailers; the tarp HAS to stay on for the module to survive. Back then the tarps were the heavy burlap cotton tarps and once they got wet they 'stuck' to the module much better than the lighter tarps do today. The challenge was keeping them attached with all the aluminum pins and rubber bungees we used before module string. That being said, there's point where nothing survives. This is @ Bayside.

module yard -

look how the wind scattered the round bales, and pushed one halfway across the field

Bayside Richardson Coop