This is related to the recent case of Rasmieh Odeh, a Palestinian activist that was found to have lied in her US citizenship application and will, according to some sources, be deported to Jordan. For example, The Daily Beast says:
If she is convicted, she faces a fine and 10 years in prison. She will then be stripped of her U.S. citizenship and deported to Jordan, where she holds citizenship.
Since most (or maybe all?) countries allow a person to cancel their citizenship, there could be a case where this kind of person only has a US citizenship (even though they are born abroad, but in a country that does not recognize "citizenship through birth").
In that kind of situation, would the person not be deported? Or would the government look for some country to accept the person even though s/he is not their citizen?