it would be possible to write a sentence like this...
Mexico accounted for more than a quarter of all foreign-born residents of the United States, having contributed large numbers of immigrants to the American population every year for the past several decades.
this sentence makes sense, because...
1/
the __ing actually applies (mexico actually has contributed large numbers of immigrants to the US),
and
2/
the __ing provides further description of/elaboration upon/explanation of the previous sentence (as is customary for comma + __ing).