No.
A limited liability company cannot own itself. If a membership interest is transferred to the company itself, for example, in a redemption transaction, that interest simply ceases to exist.
In a manager-managed limited liability company, a manager can only be appointed by a member. See Section 63.130. And, a limited liability company is defined as "an entity that is an unincorporated association that has one or more members and is organized under this chapter".
A “member” under the law is "a person with both an ownership interest in a limited liability company and all the rights and obligations of a member."
The Oregon limited liability company law requires limited liability companies to have members for various purpose, including allocation of tax liability. See Section 63.185. But under the applicable tax law, a limited liability company cannot allocate income and losses to itself. So, a limited liability company that purported to be a member would not have all of the obligations of a member under Oregon law.
Under Section 63.265 of the law, if the last member of the company ceases to be a member, for example, by dying, the person who becomes the owner of the membership interest (e.g., in the case of a death, the probate estate of the member) automatically becomes a member so that the company has members. This same section also describes transactions by which one can cease to be a member that do not have the effect of causing the company to be a member. If for some reason that couldn't happen, and a company had no members, it would be immediately dissolved by operation of law. See § 63.621(4).
The law also prohibits "shell companies", which while defined narrowly, still clarifies the legislature's intent.
While an Oregon limited liability company can be formed by someone who is not a member, called an organizer, see § 63.044, and while not all members contemplated when the company is formed need to be members initially, § 63.245, by definition, it must have at least on initial member, and without a member it can't appoint a manager and hence can't conduct business in any way.