Not sure if this works in other countries, but here in the Netherlands, homeless folks can get a postal address at municipal offices. People who move can set up (albeit paid) mail forwarding for up to a year.

Other than that, there’s good old ‘poste restante’, in which you can supposedly address mail to any post office and they’ll hold it for the recipient (even internationally), although I’ve never tried this.

(I appreciate that not everyone may actually know about these options, though.)