Thats a tough one. I was actually just buying Xboxes from ebay repairing them and selling them on ebay years ago but I am not sure if there are any direct companies that collect them.
Most times when a console is damaged they are returned to the retailer and then liquidated by the retailer to a liquidator like myself.
A way to collect damaged units is to just post classifieds offering to buy broken units for some pocket cash.