Yes, bereavement or funeral leave can be granted. I am happy to state that while offering my HR consulting services, I introduced this type of leave in two medium-sized organizations as part of employee engagement and retention initiatives. During the death of a close family member, the person should not feel pressured about work or leave consumption and should get some time to recover from the grief—this is the intention of bereavement leave.
Apart from the suggestions above, two points from my side:
1. A close family member should be defined as a spouse, children, siblings, parents, and in-laws.
2. Allow this leave to be prefixed or suffixed with CL or EL if required.