One colleague was able to use sick time at half pay to care for a terminally ill relative. Some companies allow leave without pay.
How are you "subsidizing" that?
EDIT: phrasing.
If someone is taking FMLA, the overwhelming likelihood is that they or someone they love is dying (or the opposite: they have a brand-new kid). You're worried about working a little bit harder.
Some perspective might be warranted.
Why does it have to be nuclear family members?
Not everyone has nuclear family members, or defines their family as the father/mother/brother/sister they grew up with.
In my mind, I see this as highly similar to hospitals of the past(and current) not letting members of same-sex couples visit their dying partner, because they aren't direct family or legally married.
The best course of action is to ask your employer!