Finally finally finally, I've found evidence of Matthew Madigan's death. I'd searched and search the Brooklyn Eagle for evidence thereof, and never with any luck. See how the name "Matthew" is broken across two lines? It doesn't come up in a search because of that. But when I finally thought to search for Johanna Madigan, up it popped, because her name is complete.
Let that be a lesson to you. Don't ignore anyone.
He died September 11, 1892. He was born in County Clare (Kilrush, we're told). The funeral was held at his home and at St. Mary Star of the Sea Church, and he was buried at Calvary Cemetery. No mention of his children, but likely, since he died only months after the family was recorded on the 1892 NYS Census, young Matthew and Josephine survived him.
He's listed as being 50 here, though he was said to be 51 on the 1892 NYS Census.