Cospaia was roughly only 3.3 sq km and had a population of several hundred people. It was not much bigger than modern-day Monaco and arose out of a border treaty that confused two identically-named rivers, leaving out that small area (which you gathered from the Wikipedia entry).

Returning to the negotiation table over 3 sq km was not considered worth the hassle at the time and combined with its usefulness as a 'buffer state' between Tuscany and the Papal States this led to Cospaia being left well-enough alone.

It had no army and despite its title as a republic operated as something more akin to a commune, almost anarchic. This open-ended freedom is what led the area to eventually become a haven for smugglers and other undesirables wishing to escape the laws of its neighbours.

(Most of this is from the Italian-language book Cospaia: Storia inedita della singolare repubblica)