Any country can emit a passport for any person regardless of its citizenship. Case in point, France does not recognize a passport as a proof of citizenship for its own citizen. (In BOLD here and here for french readers)
The passport is an official diplomatic documenttravel document stating to other countries that the holder is recognized as writtenspecified. Having a passport from a certain country entails some prerogatives, like being exempt of visa, or having a passport automatically purported to be valid 6 month after expiration etc....
But holding a passport and having a citizenship are in theory completely different notions, although. Although practically, 99%99.9% of the passport are issued by the country of citizenship, there are no international laws to my knowledge which prevent a country to issue a passport to non-citizen, (although some local legislation may prevent doing so.)
exemple : UK passport for Hong Kong, US passports, any diplomatic passport, which are issued on a mission basis for representation of the said State, who is sovereign in deciding who represents it....