sure it is possible. in international right there is a category of people who are not a citizens of any state. they are called apatrides.people without citizenship.
A stateless person is someone with no state or nationality, usually because the state that gave their previous nationality has ceased to exist and there is no successor state.
While more common before the 20th century, when states were somewhat more fragile entities, on September 20, 1954 the United Nations adopted the Convention relating to the Status of Stateless Persons: an active policy to prevent people becoming or remaining stateless. States which have ratified the Convention are bound to give stateless persons rights similar to those granted aliens of comparable status. Nevertheless, around nine million people still live in countries where they are not considered to be nationals, and many of them are denied access to legal protection or their rights to health care and education.
A slightly comic/tragic rendition of this condition was portrayed in the motion picture The Terminal, where a man was trapped living inside an airport because he couldn't return home due to his unrecognized citizenship status (His homeland collapsed while he was in transit). This story was based in part on the real-life story of Merhan Karimi Nasseri, who spent several years in the Charles de Gaulle Airport (Paris) due to conflicts with the French law and the fact that he was not welcome in his country of origin.
Resources: Wikipedia, UNHCR