The most common and most likely answer to this crossword clue is the 9 letter word SLUMBERED
I've seen this crossword clue in The Daily Telegraph
S
L
U
M
B
E
R
E
D
More clues leading to the result SLUMBERED
Buddy explains!

The straight part
We know that "slept" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case slept = slumbered.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.
What does SLUMBERED mean?
SLUMBERED verb- To be in a very light state of sleep, almost awake.
- To be inactive or negligent.
- To lay to sleep.
- To stun; to stupefy.