This is a STATE issue, not a CITY OF SEATTLE issue.

You need to complete an Affidavit of Loss, have it signed by ALL registered owners on the vehicle and notarized. (Most banks will notarize documents for free if you are a customer).

You then must take the signed, notarized affidavit to any vehicle licensing office and pay $4.25 for a replacement tab. If you do this at a sub-agent they will tack on an extra $5. If you do it at the King County Auditor's office it will only be $4.25. You can also do this by mail. All the information you need is found on this state website.

http://www.dol.wa.gov/vehicleregistration/replacetabs.html

In Washington, the stickers are known as "tabs" and they signify to Police that your vehicle registration is current. You need to take care of this right away.

Get the Affidavit signed and notarized and it will only cost you $4.25, instead of the full cost of re-registering the vehicle.

Ugh. What a pain. You have my sympathies.

I'm afraid you need to follow the instructions here and pay for replacements:

http://www.dol.wa.gov/vehicleregistration/replacetabs.html

I'd also add since your question has already been answered that I sort of have my doubts about the sticker being stolen. Think about it-- using a stolen tab is a pretty serious crime and you're eventually going to get caught if you get pulled over or they run your plates and see your registration isn't actually up to date. They could probably even discover it if you so much as get a parking ticket! I don't really see anyone doing that just to avoid an expired tag ticket.

Plus those stupid stickers fall off all the damn time if you don't thoroughly clean the plate and apply the sticker with loving care.