The most common and most likely answer to this crossword clue is the 11 letter word SYMPATHETIC
I've seen this crossword clue in The Guardian
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More clues leading to the result SYMPATHETIC
Buddy explains!

The straight part
We know that "Supportive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case supportive = sympathetic.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 SYMPATHETIC mean?
SYMPATHETIC adjective- Of, related to, showing, or characterized by sympathy
- Relating to similarity
- Relating to the sympathetic nervous system
- Relating to sounds induced by vibrations conveyed through a fluid or gas from a body already in vibration.
- Of magic, a supernatural connection or power resulting from two items having the same form or some other correspondence.