Incorrect sentence.
Corrected sentence: Last night, Jason introduced me to a friend of his, whose hair went all the way down to the back of his knees in a single dreadlock.
The period before the word "whose" in the original creates a fragment "Whose hair was all the way down to..." This is a phrase which is describing "a friend of his" and should be included in the same sentence. So you simply separate it by a period.