The most common and most likely answer to this crossword clue is the 3 plus 3 plus 5 letter word THE BIG SLEEP
I've seen this crossword clue in The Daily Telegraph
T
H
E
B
I
G
S
L
E
E
P
More clues leading to the result THE BIG SLEEP
Buddy explains!
The straight part
We know that "Story one may mistakenly associate with ‘Rip Van Winkle’" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case story one may mistakenly associate with ‘rip van winkle’ = the big sleep.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.