The most common and most likely answer to this crossword clue is the 6 letter word NABOBS
I've seen this crossword clue in The Daily Telegraph
N
A
B
O
B
S
More clues leading to the result NABOBS
Buddy explains!

The straight part
We know that "very rich men" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very rich men = nabobs.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 NABOBS mean?
NABOBS noun- An Indian ruler within the Mogul empire.
- (by extension) Someone of great wealth or importance.
- (by extension) A person with a grandiose style or manner.