A Full Admin can process a proxy registration on behalf of a household, even if cash or check payments are not enabled for the public. During the proxy registration process, the Admin will have access to all payment methods, including cash and check.
If you want to allow an individual member to pay by cash or check without enabling this option for everyone, simply complete a proxy registration for them and select cash/check at checkout. Additionally, if a household debit has been paid in cash or by check, you will need to go through proxy registration and check out to mark the payment as completed. For more details, see Proxy or Manual Registrations in Program Registration.