The most common and most likely answer to this crossword clue is the 12 letter word PARTICIPATED
I've seen this crossword clue in The Daily Telegraph
P
A
R
T
I
C
I
P
A
T
E
D
More clues leading to the result PARTICIPATED
Buddy explains!

The straight part
We know that "became involved" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case became involved = participated.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 PARTICIPATED mean?
PARTICIPATED verb- To join in, to take part, to involve oneself (in something).
- To share, share in (something).
- To share (something) with others; to transfer (something) to or unto others.