The most common and most likely answer to this crossword clue is the 11 letter word UNCONVINCED
I've seen this crossword clue in The Daily Telegraph
U
N
C
O
N
V
I
N
C
E
D
Buddy explains!

The straight part
We know that "Dubious" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dubious = unconvinced.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 UNCONVINCED mean?
UNCONVINCED adjective- Not convinced or lacking conviction
- To cause to abandon a conviction.