The most common and most likely answer to this crossword clue is the 4 letter word FIDO
I've seen this crossword clue in The Guardian
F
I
D
O
Buddy explains!

The straight part
We know that "dog" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dog = fido.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 FIDO mean?
FIDO noun- A coin that is defective, having been incorrectly minted, often prized by collectors.