If you scroll down the list, there are a few apartments listed that allow sex offenders and other programs as well.
https://www.housingconnector.com - You can take their free community partner training to be able to refer people to Housing Connector. This allows you to search Zillow for rentals that accept Housing Connector, which allows participants to have up to $3000 in back rent, up to 3 evictions, can waive credit checks, application fees, and criminal background searches, depending on the property. They also provide the participant with two years of housing stability support, including mediation, conflict resolution, and legal resources; will assist the participant with rent if they are unable to pay rent for one month; and offer up to $5000 in risk mitigation, so landlords are more likely to work with individuals on properties they would not otherwise work with. You can find out more information at the link provided.
I'm not sure what level of sex offender your person is, but here are some Transitional Housing that accept different levels of sex offenders that I found.
ABSTINENCE HOUSING AND HUMAN SERVICES (253) 709-9192 Days/Hours: Daily: 8am-5pm Housing is located in South King County. Description: Provides a recovery program for individuals suffering from drug and alcohol addiction. Drug or alcohol use is not tolerated and residents must be seeking to be clean and sober and in recovery. Eligibility: Individuals recovering from drug and alcohol addiction. Must be clean and sober for 72 hours before applying. Maintains a clean and sober, zero-tolerance policy for residence. Does not accept those with a level II or III sex offense. To Apply: Call to inquire about availability Fees: Call to inquire.
HOUSE OF MERCY MINISTRIES (206) 651-7840 or email: office@hom.church Multiple locations in King County Description: Offers a faith-based transition program for recovering addicts, homeless individuals and successful re-entry into society for those being released from prison. Operates 15 residential programs in King County, one in Pierce County, and one in Spokane. Offers employment assistance through a network of supporting employers and organizations. Also assists residents in fulfilling DOC requirements, obtaining driver's licenses and ID cards, food stamps and public assistance, resume preparation and employment resources, and other items necessary for successful re-entry into society. Eligibility: Men who are recovering addicts, homeless, or being released from prison. Days/Hours: M-F: 8am-4:30pm. To Apply: Obtain an application form online, by calling or via email at contact@houseofmercyministries.net. Sex Offenders: Yes
PIONEER HUMAN SERVICES – TRANSITIONAL RESIDENTIAL RECOVERY http://pioneerhumanservices.org/housing/transitional (206) 624-0082, Ext. 104 Days/Hours: M-F: 8am-4pm Description: Offers low-cost drug and alcohol-free transitional housing to those who are having difficulty obtaining housing due to a criminal record or in a treatment program for a substance use disorder. Facilities are conveniently located near bus lines and within walking distance to shopping and other community service providers. Random drug and alcohol tests are given at all facilities. Eligibility: Individuals who have been recently incarcerated or in a treatment program for chemical dependency issues. Must be committed to clean and sober living. Cannot accept those with a history of arson. To Apply: Download application from specific property on website. Submit application in person to specified address on application. Mail or fax if currently incarcerated.
STEVENSON HOUSE* (206) 767-4055 Days/Hours: M-F: 10am-6pm, S: 12-4pm Description: Provides studio and sleeping rooms (no cooking facilities). Those with level I level III sex offenses may apply, but must be out in the community for at least 6 months before applying. Stephenson house reserves the option to contact the Department of Corrections as a part of their applicant screening process. To Apply: Call for screening.