The most common and most likely answer to this crossword clue is the 10 letter word MORATORIUM
I've seen this crossword clue in The Daily Telegraph
M
O
R
A
T
O
R
I
U
M
More clues leading to the result MORATORIUM
Buddy explains!

The straight part
We know that "Stay" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stay = moratorium.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 MORATORIUM mean?
MORATORIUM noun- An authorization to a debtor, permitting temporary suspension of payments.
- A suspension of an ongoing activity.