If I'm borrowing your car, and some guy comes along who loves that car and offers you 5x what you paid, do I just have the right to keep your car indefinitely because it's somehow "mine" by virtue of having borrowed it initially?  Even if I gas it up and run it through the car wash to keep it nice, it's still your car.

The basic protection is already there - the rental contract.  The owner can't kick you out during the term of the contract.  There is not anything in Oregon law that prevents a longer-term lease if you can negotiate it.