Hi there Peter,
Are you aware that the Workhouse/Blackwell's Island was a prison? Jackson Dempster is listed as a prisoner there in 1880.
However I do find him in the City Directories for NY, starting in 1872 and up to 1888 at various addresses. Which tells me he either didn't spend long in prison or he actually worked there and is erroneously enumerated as a prisoner???
Here are Directory listings, found on Footnote.com:
1872- 220 First Av.; baker
1873- h[ouse] r[ear] 435 E 12th, baker
1875- h. 263 E 10th, baker
1877- Not listed
1878- h. r. 506 E 14th, baker
1880- h. r. 506 E 14th, baker
1885- h. r. 506 E 14th, baker
1888- h. 421 E 16th, baker
These addresses are indeed in Manhattan. No sign of Nancy anywhere. There was a Nancy Dempster in Elgin, Kane Co., Illinois, a 30 yr. old married housewife, residing in an insane asylum, bplace: Ireland. It seems unlikely that this is his Nancy.
I don't see anything for Jackson after 1888. I don't know if this is any help. I don't really have any information on burials in NY. I do have a book about cemeteries in NY but not listings of actual burials. There are so many possibilities where Jackson might be buried, my only suggestion would be to write to the big ones and hope to find them.
Best of luck.