The times I've seen solicitations for donations for funeral expenses have been in situations where the death was either unexpected or where there was a drawn out illness and therefore a lot of medical expenses that need to be paid as well. Most of the time, sad to say, it's a child who's died.
I also usually don't see requests for straight-up donations, though. What seems to be common around here are fundraising events. When my cousin's daughter died (she was 13 and the death was a suicide, so it was very unexpected), they had a fundraiser at a bar owned by a friend. The bar donated a keg of beer, and organizers (my aunt - the child's grandmother - and friends of the family) provided bbq, chips, etc. The suggested donation was $10, which got you unlimited food, pop, and free beer. (There was also a cash bar, but that money did not go to the family.) I've seen notices of similar types of fundraisers for funeral and medical expenses, and I really don't think there's anything wrong with them. The people who donate are getting something in return, which is always a bonus, and they tend to happen in situations where it's a large, unexpected expense that the family probably couldn't otherwise handle.