Actually not in Oregon. I found this out the hard way. If you move, you have to notify the Elections Dept in the county you live in and give them your new address, the PO will not forward ballots.
In WA State, they forward ballots. They have always forwarded absentee ballots, so they just continued the practice when they went to all mail. It creates a real mess.
When we were in a temporary rental while building, we each received two ballots, but then so did everyone else that we knew, so that was no surprise.
Then when we moved in to our new house, we called and changed the address for my husband, myself and my daughter. Then for a primary election, they sent my daughter a ballot for the election in our old district. When I called and checked on it, they told me that she could go ahead and vote in it, if she wanted to, since she had the ballot.