The backplate is a separate item that you buy or you make. Nobody sells new chucks with a backplate because they don't know what lathe you have.?

Go to littlemachineshop.com and buy a backplate for about 30 bucks (for 4") or up, then turn it to match your spindle and chuck and you are done.?

As for the chuck, just do a search on eBay for K72-xxx where xxx is the diameter in millimeters. So, it is 100mm for 4", 125 for 5" and 150 for 6" chucks. The prices I found with great ease start at $59 and go up from there.

Instead of complaining about it, just do the legwork. I spoon fed you all the information you need to find your chuck/plate combo.?