I'm in Maryland not Texas and no, trash isn't required to have registration but I think I haven't been clear on the situation...
I have a 95 K75 with 107K that is currently registered, but it was in a front-end accident 11 years ago that broke off the stops that prevent the fork tubes from bashing into the tank when locking the bars left/right. I didn't see the damage till after I'd accepted the fixed bike and left Seattle for the East Coast. I welded some nubs on the frame to emulate the stops that broke off, but I have reason to believe it wasn't the only damage, despite the fact that I've been riding it like that for 11 years. Risky, I know, but I had little choice because I had to ride but didn't have any $$ for a new bike or a workshop to fix the old one in. Anyway, the dealer who did the repair said it was safe to ride, whatever that's worth, so ride I did.
Last year I bought a 94 K75 with 174k on the clock. It had some goodies I need (Ohlins shock, Bruno-ified FD and DS, etc...), so I paid the PO what he was asking ($1500) and bought it for the purpose of putting the 95 engine and drivetrain on the accident-free, undamaged 94 frame and selling the duplicate parts to the K75 community at a good price.
So that's where I am now. When I'm done, I'll have a K75 with a 1995 107K engine on an undamaged, unregistered 1994 frame. The registered, damaged 1995 frame will be trashed, as it should have been after the accident in 2005. I'll have to pay to register the undamaged 1994 frame to make it legal. Once I do that, I intend to put another 100k on it at least, so it will be worth the $$ I'll need to pay to register it...I just dont' particularly like spending $$ so I am hereby bitching about it.
Make sense?