The most common and most likely answer to this crossword clue is the 10 letter word SQUEEZABLE
I've seen this crossword clue in The Guardian
S
Q
U
E
E
Z
A
B
L
E
Buddy explains!
The straight part
We know that "Compressible/object inviting a hug" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case compressible/object inviting a hug = squeezable.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.