Someone asked why you would want to run the lathe motor and spindle in reverse. The first would be using a tool-post grinder. I would classify this as safe to do as as it takes considerably more torque to to break the chuck threads loose than it does to finish nu-screwing the chuck for removal.
The second is any case where the carriage drive must remain engaged for the duration of the operation, such as most metric threading with an inch-based lead screw. When the pass is complete, you back the cutter out a few thou and reverse the motor to back the carriage out.
The third (mentioned by someone else here) is power tapping with the tap mounted in the headstock, But for that you use a 2Mt or 3MT collet instead of a chuck. And you would have to rig up some way to hold the work piece.
And the fourth would be power tapping with the tap mounted in the tailstock,