Is there a link(s) where I can look up a NYC resident to see if they
are collecting unemployment insurance?

I doubt that such a thing exists. I used to work in an office (in
another state) which kept records of unemployment insurance. We were
not permitted to acknowledge that a person was receiving benefits,
unless we were dealing with the client himself or with the employer
whose account was involved.

Thanks for the comment.  I really appreciate it.  I'll close the question. 
Again, thank you very much.