A person or thing that makes something foul or contaminates it.
From 'befoul' plus '-er' suffix (Old English origin), which creates agent nouns—someone or something that performs the action of the verb.
The '-er' suffix is one of English's most productive morphemes—almost any transitive verb can become 'a [verb]-er who does that action,' which is why we easily accept 'befouler' even if it's archaic.
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