Never heard/read the expression/term but as a guess, if it's the opposite of "keeper" (in terms of romance or a relationship, one of the opposite sex a person would be attracted to), the term "dumper" could be reference to a person one would not want to continue a relationship with.
Or it could be an extension of the expression 'to dump on someone', so that a dumper would be a person who, in the words of the song, 'ha a tendency to dump on you'. That seems possible, but I've never met the expression.
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