Increasingly sick murderer losing head (5)

I believe the answer is:

iller

I'm a little stuck... Click here to teach me more about this clue!

'increasingly sick murderer losing head' is the definition.
I can't tell whether this defines the answer.

'murderer losing head' is the wordplay.
'murderer' becomes 'killer' (I've seen this before).
'losing head' means to remove the first letter.
'killer' with its initial letter removed is 'ILLER'.

Can you help me to learn more?

(Other definitions for iller that I've seen before include "In worse health" , "Even more 9" , "Less well" .)

I've seen this clue in The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.