In the second pattern, the subject complement would be the past participle of a transitive verb.
Place the paper on the table.
The paper is placed on the table.
Lay transitive the paper on the table.
The past participle of to lay is laid.
The paper is|was laid on the table.
Someone lays present the paper on the desk each morning.
Someone laid past the paper on the desk.
Someone has laid present perfect the paper on the desk.