In my lucrative experience with having to run a lift on a diet and making observations while working in lift operations when I worked in the industry, it usually signifies some sort of power troubles or electric drive issues. As the amount of load increases (the number of people), the more power or amperage is required to push or pull that load up the hill. A lift’s electric drive monitors the speed of the lift and if it detects that the speed is slower or faster then the set speed, it will adjust the amperage to the motor as necessary. More people, means it takes more energy to move those people. The electric drive will continue to increase the amperage until it reaches the set speed or something faults out. A lift “faulting out” is basically the lift’s safety systems functioning to stop the lift before it any possible damage happens to the motor - effectively trying to stop an issue before it becomes an issue.
By placing the lift on a diet, you can limit the amperage necessary to run the lift and therefore limit the faulting out until a solution is found for the issue. This is usually done to either operate the lift until the end of the day at which point it can be fixed, or run it until a part comes in from the manufacturer.
As for the “is it safe to ride” part of the question, I would say that it is based on what I said above. With a drive faulting out, or it not being able to push/pull a full load, all it’s going to do is stop. Then if there’s an issue getting it going again, lift maintenance will usually run people off on auxiliary power. It’s only in extenuating circumstances that a lift would need to be rope evac’d.