The most common and most likely answer to this crossword clue is the 10 letter word INBREEDING
I've seen this crossword clue in The Times
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More clues leading to the result INBREEDING
Buddy explains!

The straight part
We know that "a cause of some illnesses" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a cause of some illnesses = inbreeding.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 INBREEDING mean?
INBREEDING verb- To breed or reproduce with those that are related.
- To breed with those that share common traits or qualities.
- To produce or generate within.
- Breeding between members of a relatively small population, especially one in which most members are related