Very uneducated post here.
If there is a problem, at all, in the ride area, it's the operators duty to stop. Certain parks are more relaxed about things, but just about everywhere, if someones in the ride area and the operator/attendants see a problem, the ride will immediately be stopped.
Most ride systems do not have built in brakes on the train, so no, if the ride is past a lift hill or brake run it won't stop until the next block section because it just runs on gravity.
With incidents like the batman decapitation the ride operator had no control of what happened if the guy jumped the fence after the carriage left the lift hill. The rides run on momentum and has nothing to stop its trains. But there are blind spots on rides and if people are dumb enough to enter the ride area in the first place, it's their problem. They are literally putting their life on the line, and if the operator can't have the power to stop the ride, it's their own fault.