Ask the court for an alternate method of service.
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Nothing requires a tenant (or anyone) to answer the door for a process server. What you heard is generally correct. Posting the summons and complaint after getting the court's permission will enable you to regain possession of the property but will limit your opportunity to recover any money. There are ways around this, but you'll probably have to invest in a lawyer to get it done. After this answer I'm posting a link to the statute which pertains to obtaining court's permission to post the summons and complaint, RCW 59.18.055.
This answer is intended as a courtesy only, and does not constitute an attorney-client relationship between the attorney and the questioner.
When a sheriff deputy knocks on the door, most persons open the door rather promptly. In King County, the sheriff department will serve legal documents for a fee.
The tenant can be personally served anywhere. Your process server can serve the tenant at her work, on her way to the grocery store, when she takes out the garbage, etc.
Some process servers get creative. For example, they pretend to be delivering flowers, packages, etc.
As long as the means used by the process server is not unlawful, personal service likely will be effective regardless what tricks the server uses to have the defendant open the door.
If the tenant has not been paying rent, you likely will never see the rent anyway. So, not being able to get a judgment for rent owed may not leave you any worse off than if you can have the tenant personally served.