Washington state recognizes that lots of people do not actually have a written agreement regarding their tenancies. If you want to sublet out your current place, you want to discuss this with your current landlord first, before making any irrevocable moves, such as moving in a sub-tenant without permission.
The thing is that when there is no writing, either party can end the tenancy with 20 day's notice properly given to the other party (RCW 59 18 200). If your current landlord doesn't appreciate your plan, you can easily lose your current tenancy. If that is an issue for you, discuss what you want to do with your landlord first.
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My guess is that you still HAVE a written contract, if you ever had one. Most leases provide that the contract continues, (sometimes referred to as the tenant "holding over"), after the expiration of the original lease term. You will need to either read your contract or have an attorney review it for you to determine what it says about sub-leasing. Most leases require the landlord to approve such arrangements, in advance. That does not mean that you cannot do this, but you may have to jump through a couple of hoops, first.
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