Worth stating in full generality: it does not matter which version of haber you use, even the "to" form itself. The verb after it always takes -ado or -ido.
Me gustaría haber ido (I would like to have gone)
Just as in English, where I have sold gives it is sold and I have lost gives I am lost. This hands you hundreds of adjectives.
After haber it is always cerrado, whatever the object. As an adjective it agrees in gender and number like any other.
Estoy perdido / perdida · Está terminado · Está terminada · Están vendidos · Están vendidas
A rare simplification: with this particular type of adjective you do not need to weigh state against characteristic. They go with estar, with a couple of exceptions.
Está cerrado · Está cerrada · Está hecho · Está abierto
The exception that explains the persona trick from earlier. When you say what something is, giving it its name, nothing could be more characteristic, so you use ser. The adjective riding along is secondary.
Es una persona cerrada · Es una persona perdida · Es una persona feliz
So es cerrado alone sounds like a mistake, but es una persona cerrada is fine, because es is going with persona.
Está cerrado a la idea (he is closed to the idea)
Cansado is not a standalone word: it is cansar, to tire, in its after-haber form.
As with the other reflexives, it does not literally mean you are responsible for tiring yourself.
La he cerrado (referring to la puerta) · Está terminada (la película)