How we fail public health eventually? Refuse to pay (5)

I believe the answer is:

welch

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

'refuse to pay' is the definition.
I can't judge whether this definition defines the answer.

'how we fail public health eventually?' is the wordplay.
'eventually?' says to take the final letters (I've seen 'eventually' mean this).
The last letters of 'how we fail public health' are 'WELCH'.

Can you help me to learn more?

(Other definitions for welch that I've seen before include "Renege on obligation" , "Decamp without paying" .)

I've seen this clue in The Irish Times.

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