The most common and most likely answer to this crossword clue is the 8 letter word COARSEST
I've seen this crossword clue in The Guardian
C
O
A
R
S
E
S
T
Buddy explains!

The straight part
We know that "Most vulgar" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most vulgar = coarsest.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 COARSEST mean?
COARSEST adjective- Composed of large parts or particles; of inferior quality or appearance; not fine in material or close in texture.
- Lacking refinement, taste or delicacy.