Jenava, it's definitely imperfect but they address this on the voter registration page: http://www.kingcounty.gov/elec.....ation.aspx
"Non-traditional residential addresses/homeless voters
The Washington Constitution doesn’t require a "residence" as a condition of voting as long as a person meets all other registration requirements. (Article VI Section1)
Voters who lack a traditional residential address can register at the shelter, park, motor home, intersection or other identifiable location they consider their residence. This location will be used to determine which precinct they will vote in. (RCW 29A.08.112 effective 2005)
Along with your residential address, you must also provide a valid mailing address. An accurate, valid mailing address is essential in order to receive ballots and election information on time. This can include a post office box, address of a friend or relative, shelter, or general delivery at a local post office."