An non-native English-speaking friend of mine came across the phrase "not unknown to" as in "tragedy is not unknown to the Kennedy family" and asked the question, "What's the difference between 'not unknown' and 'known'?" The phrasing "tragedy is known to the Kennedy family" is logically equivalent, and the best answer I could come up with is perhaps "not unknown" is a literary device used for impact. Any thoughts on the difference between the two ("not unknown" is perhaps an older or particular style of writing or has a history in British English?).
This is an example of the rhetorical device known as litotes. This involves a careful (rather than unconsidered) negation of a negative, often for reasons of style.
Here, 'tragedy is known to the Kennedy family', though grammatical, sounds unusual. 'The Kennedy family have known their share of tragedy' is more idiomatic, as is 'tragedy is not unknown to the Kennedy family' (which, being an obvious vast understatement and hence incongruous, generates emphasis).