The most common and most likely answer to this crossword clue is the 9 letter word OUTWORKER
I've seen this crossword clue in The Guardian
O
U
T
W
O
R
K
E
R
Buddy explains!

The straight part
We know that "this one stays at home" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case this one stays at home = outworker.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 OUTWORKER mean?
OUTWORKER noun- A subcontractor who carries out work at an off-site facility.
- One who works outdoors.
- One who takes away work to do at home.