While not an orphan, the Haskell Free Library and Opera House<http://www.atlasobscura.com/places/haskell-free-library-and-opera-house> is an interesting border case.

http://www.atlasobscura.com/articles/the-us-canada-border-runs-through-this-tiny-library

From: Maps-L: Map Librarians, etc. [mailto:[log in to unmask]] On Behalf Of Zellmer, Linda
Sent: Thursday, June 01, 2017 12:10 PM
To: [log in to unmask]
Subject: Orphans of the Atlas

Hello,
Illinois also has one, and it turns out that it was Illinois' first state capital -- Kaskaskia, Illinois.It can only be reached by driving into Missouri. The channel of the Mississippi River changed after floods in the 1880s, and the town ended up stranded west of the river.
Linda Zellmer
--
Linda Zellmer
Government Information & Data Services Librarian
Liaison to Natural Sciences & Agriculture
415 Malpass Library
Macomb, IL 61455
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Phone: 309-298-2723<callto:309-298-2723>
Fax: 309-298-2791<callto:309-298-2791>