Could not find any similar suggestion anywhere, so I'm gonna drop it right here.
Cops need to have a cool down to pick up a money bag dropped by a criminal who died. As an example, I was chasing a suspect who had a money bag and I wanted that bag for myself. I chase him down, a cop interferes, manages to kill him, and whilst I'm shooting the cop, he takes the bag dropped by the suspect and I get nothing for myself.
By looking at the situation above, it should be the way that if a cop is recently shot at, they can not pick up money bags dropped around them. About the cool down, it may be the same as the seconds to wait when entering/exiting an interior after being shot.