On my BL12-24 (and presumably their look alikes, Warco BH600, Chester Craftsman etc) behind the regicster is flange. On the back of the chuck is an extension with two diametrically opposed M8 tappings.
These are used to secure two dogs which hook behind the flange, so that IF the chuck tried to unscrew, the dogs would prevent any forward movement.
Retrofitting something like this for a Myford, or similar lathes, might be more difficult, but worth exploring.
I would not be keen on just using a grubscrew, because of the risk of danage to the thread or register, but a setscrew with a plain end, inro a shallow drilling, might be effective.
When I had a ML7, I did not have a problem with chucks coming loose when reverse running (But being aware of the risk was careful) Lathes with heavy braking facilities, can cause this sort of problem.
(Not long ago, I read of someone saying that he had a chuck land in his lap! Fortunately, from a small lathe)
Howard