To steal from or pilfer, possibly making someone filthy in the process of theft.
Combination of 'be-' prefix and 'filch' (to steal or pilch, meaning to plunder). 'Filch' itself may derive from Old English or Scandinavian sources meaning to seize. The 'be-' intensifies or transforms the base verb.
The 'be-' prefix in words like 'befilch' often acted as an intensifier—it didn't just mean the action, but emphasized *becoming* affected by it or thoroughly experiencing it, so 'befilch' might have meant not just to steal from someone but to thoroughly rob them.
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