The most common and most likely answer to this crossword clue is the 10 letter word DEGENERACY
I've seen this crossword clue in The Times
D
E
G
E
N
E
R
A
C
Y
More clues leading to the result DEGENERACY
Buddy explains!

The straight part
We know that "immorality" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case immorality = degeneracy.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 DEGENERACY mean?
DEGENERACY noun- The state of being degenerate (in all senses)
- The ability of one part of the brain to take over another's function without being overexerted.