A person who duns; a creditor or debt collector who makes persistent demands for payment.
From the verb 'dun' (to make persistent demands) plus the agent suffix '-ster'. The -ster suffix historically created occupational nouns (like 'spinster' or 'gangster'), and here applied to describe someone whose job is demanding payment.
The suffix '-ster' was once wildly productive for making occupation words—we've mostly forgotten it, but it's hidden in 'gangster,' 'hipster,' and 'youngster,' and 'dunster' shows how every job, no matter how disliked, got its own -ster name in medieval times.
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