Perhaps one’s undoing last of aspirin, being sick (7)

I believe the answer is:

nemesis

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'perhaps one's undoing' is the definition.
I can't tell whether this definition defines the answer.

'last of aspirin being sick' is the wordplay.
'last of' suggests the final letters.
'being sick' becomes 'emesis' (I've seen this before).
The final letter of 'aspirin' is 'n'.
'n'+'emesis'='NEMESIS'

Can you help me to learn more?

(Other definitions for nemesis that I've seen before include "curse" , "Come-uppance" , "Fate" , "Retribution personified" , "Siemens (anag.)" .)

I've seen this clue in The Times.

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