Today my rear left driveshaft gave up (lots of grinding noise while in Drive or Reverse, coming from the left side of the differential, and the car won't move).

One strange thing I noticed is that the car will not stay still when it's in Park. I have to engage the e-brake to stop it from rolling up or down.

Is this related to the broken driveshaft? 

The car is RWD with automatic transmission.