Read rest of the answer. Keeping this in consideration, what's a word for closed off?
roped off. exp. , v. closed. frozen. sealed.
One may also ask, what is closed off? Definition of close off. : to not allow (something) to be used for a period of time : close The city closed off the beach to tourists. Half of the museum was closed off while they made the changes. —sometimes used figurativelyHe closes himself off to new experiences.
Then, what do you call a person who is closed off?
adjective. having or showing little or no emotion: apathetic behavior. not interested or concerned; indifferent or unresponsive: an apathetic audience.
What is the synonym of private?
secret, private(adj) not expressed. "secret (or private) thoughts" Synonyms: underground, occult, private, surreptitious, individual(a), undercover, hugger-mugger, hush-hush, secret, mysterious, mystic, hidden, privy, clandestine, secluded, cloak-and-dagger, orphic, unavowed, confidential, hole-and-corner(a), mystical.