The most common and most likely answer to this crossword clue is the 6 plus 7 letter word GERMAN MEASLES
I've seen this crossword clue in The Guardian
G
E
R
M
A
N
M
E
A
S
L
E
S
More clues leading to the result GERMAN MEASLES
- In the wake of micro-organism there’s a nameless horrible disease
- Illness caused by bug — one given various names by the French
- Bug set off a nameless illness
- A nameless germ spreading disease
- Virus leads to a development of lameness producing complaint
- Disease from microbe, a nameless disorder
- Bug with exotic name like ‘the Continental Disease’
Buddy explains!

The straight part
We know that "Illness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case illness = german measles.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.