Can a registered sex offender emigrate to another country without a sex offender registry?

In the state of NY, is it possible to emigrate from the country while being a Risk Level 1 sex offender to a country with no sex offender registry? Also, if the individual does emigrate, will he have to follow the United States sex offender registry guideline and still write back his address once a year and return to the country to take a picture every three years? Or will he have to follow the rules of his new host country. If the individual surrenders his American citizenship to obtain the citizenship in his new host country, will the crime/sex offender records ever be retrievable?