Illegitimate?
 

I manage a tree for a friend and cannot find ANYONE linked to her paternal grandfather (grandparents separated when her father was a small boy - and only child)

I have a closed DNA group 23 - 70 cM linked only to themselves of five members.

Given that I'm looking for a quarter of her ancestry, should the sample be slightly larger in size?

I suppose it would depend on how many relatives of her grandfather have taken DNA tests.

Indeed. Life is so much more difficult when you have singleton children.