The most common and most likely answer to this crossword clue is the 7 letter word PROPPED
I've seen this crossword clue in The Times
P
R
O
P
P
E
D
More clues leading to the result PROPPED
Buddy explains!

The straight part
We know that "Supported" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case supported = propped.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 PROPPED mean?
PROPPED verb- (sometimes figurative) To support or shore up something.
- To play rugby in the prop position
- (usually with "up" - see prop up) To position the feet of (a person) while sitting, lying down, or reclining so that the knees are elevated at a higher level.
- To manually start the engine of a propeller-driven aircraft with no electric starter by pulling vigorously on one of the propeller blades using the hands, so that the propeller can catch ignition.