I think it all depends on how close the relationship was with this family member.
My dad passes away last Sunday. I cried but didn't grieve. Dad was very, very ill - he had no legs, heat complications, was fed oxygen daily, lungs fulling up with water, very poor eyesight etc. He was suffering and Mum was also suffering to care for him, she had no help what so ever. We all have to die, and in dad's situation I think it's better he rest his soul than to suffer to live.
So to answer your question, it all depends on the situation also.