Is it illegal to possess a motorcycle frame with the neck cut off?

No. The neck is usually cut off when a replacement frame for that motorcycle has been supplied by the manufacturer. Usually due to frame damage sustained in an accident. The neck has the serial number stamped on it, and the manufacturer usually requires the old neck to be returned in order to ensure that there are not two motorcycles with the same serial number. So the old frame without a neck is trash, junk...and probably not straight. Unless, of course, you stole the frame. Then it is illegal. Never try to rebuild a motorcycle with a frame that has had it's neck removed...unless you have a frame table that would allow you to install a new neck precisely and straighten the other damage on the frame. It would be very dangerous to ride a motorcycle with a crooked frame or neck.