I concur in regard to the potential for a broken shaft.
However
There are other possibilities that I have seen.
1)
Oil pump is worn and lost it's prime. You can sometimes get them to start pumping again by temporarily overfilling the crankcase by 4-5 quarts to submerge the entire pump in
oil.
2)
Oil pump Pick-up gasket got sucked in and the oil pump is now sucking air from the crankcase. Again - like temporarily over filling the crankcase - you can see if she now sucks oil in.
You will want to do these operations with a drill motor and dummy distributor or primer shaft.
Good luck!