The USA is different from (almost) everywhere else, so saying in the USA/for tax purposes is usually not helpful to anyone other than an American (not being snippy, just FYI).
It does depend on the country, but IMHO unless you become actually resident somewhere else, your last country of residency stays 'it' for all other countries. THAT country may think differently (but are unlikely to turn down tax due!).
A person needs an address, for all sorts of reasons. PO Box isn't ideal but it'll do (especially in N America if you put #123 rather than PO Box 123). But, when setting up a mailbox you'll need to give them a real address...