There are plenty of exclaves with country borders out there. For instance, here's a bit of Germany inside Switzerland:
https://goo.gl/maps/bw3PwD19JhR2
The village is called Büsingen.
https://en.wikipedia.org/wiki/B%C3%BCsingen_am_Hochrhein
In United Arab Emirates there is an Omanian exclave called Madha, which in turn contains a UAE exclave called Nahwa:
https://goo.gl/maps/REXtsfb3gHs
https://en.wikipedia.org/wiki/Nahwa
And there's even one third-order enclave.
https://en.wikipedia.org/wiki/Dahala_Khagrabari
Dahala Khagrabari is a piece of India, surrounded by Bangladesh, surreounded by India, surrounded by Bangladesh.
And things stay this way because it is quite awkward to change places where people live to belong to another nation - however impractical these exclaves may be.