depends on the person, but my 2p
One of my direct reports; his wife was taken ill last week and had to go into hospital, where she has now been stabilised and finally yesterday had a stone removed from a bile duct. They have an older son (10 or 11 now) a 7 year old daughter and a 3mo baby.
My report asked if he could have short notice holiday from next year’s entitlement as all this year’s is gone apart from Christmas. I tore him a new hole for even asking. In circumstances like this I told him, he should do the important stuff for his wife and kids, and then if he has spare time ensure nothing goes so badly wrong that he can’t pick it up when things get back to normal, and that anything that can’t be done in the meantime either delegate it back up to me or palm it off to one of his colleagues. I know he’ll make as much time up as he needs to in order to keep the boat afloat so i can trust him with it.
In any case, in a situation like this I’d be so distracted i’d be a liability at making any important decisions.
It might be different re: how closely I’d watch the situation if it were another of my reports but I’d still give the time off for free without question. If a manager can’t see this, they shouldn’t be managing.