The most common and most likely answer to this crossword clue is the 9 letter word PAILLASSE
P
A
I
L
L
A
S
S
E
Buddy explains!
The straight part
We know that "sleep on this" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sleep on this = paillasse.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 PAILLASSE mean?
PAILLASSE noun- An under bed or mattress of straw.