Answer: It is unclear to me whether your complaint is with the housing authority running the voucher program or the tenant using the program.
I do not recommend you refusing to allow Section 8 housing applicants. ORS 59A.421 (Discrimination in selling, renting or leasing real property prohibited) provides:
(2) A person may not, because of the race, color, religion, sex, sexual orientation, national origin, marital status, familial status or source of income of any person:
(a) Refuse to sell, lease or rent any real property to a purchaser. This paragraph does not prevent a person from refusing to lease or rent real property to a prospective renter or prospective lessee:
(A) Based upon the past conduct of a prospective renter or prospective lessee provided the refusal to lease or rent based on past conduct is consistent with local, state and federal law, including but not limited to fair housing laws; or
(B) Based upon the prospective renter's or prospective lessee's inability to pay rent, taking into account the value of the prospective renter's or prospective lessee's local, state and federal housing assistance, provided the refusal to lease or rent based on inability to pay rent is consistent with local, state and federal law, including but not limited to fair housing laws. (Emphasis added.)
This means that landlords it is permissible to screen and reject any applicant, including those with a Section 8 voucher, for past conduct and ability to pay rent. But they may not be rejected simply because they use Section 8 vouchers.
There is a required contract between the landlord and the public housing authority (called the Housing Assistance Payment Contractor "HAP Contract"), which lists the landlord's rights and responsibilities. Part of he HAP Contract, called the Tenancy Addendum, becomes a part of he rental agreement between the Section 8 tenant and the landlord.
The local housing authority does not guarantee the tenant's performance, and will not have screened the applicant for his or her suitability as a tenant - that is the landlord's responsibility. However, a Section 8 voucher tenant's failure to pay his or her portion of the rent or to comply with rules regarding maintenance of the property can lead to termination of the tenant from the Section 8 voucher program.
There are two sources of rental payments; the tenant pays approximately 30%-40% percent of the rent (with some exceptions) and the housing authority pays the balance. This leads me to believe that your issue is with the tenant, not the program. If the tenant is blaming the program, that is something they need to take up with the housing authority. If you are not getting the rent payments from the housing authority you should contact them.
A tenant's failure to pay their share of the rent, or being consistently late, can jeopardize their right to continue to receive a Section 8 voucher. You are not required to accept partial rent. If the public authority pays its share, but the tenant does not, you may file for eviction. However, before doing so, you should contact an attorney familiar with Section 8 housing issues.