Is there a passive for the sentence "Be quiet."?

Quiet is a predicate adjective, and almost all predicate adjectives are intransitive. Passive can only apply to a transitive predicate.

Be is an auxiliary verb, required to hold the tense for the predicate adjective; no auxiliary verb ever governs Passive. Indeed, the Passive construction uses be itself.

It seems like "Silence would be appreciated." captures the meaning without being a command.

Try this:

The unruly class was quieted down by the teacher sharply whacking her yardstick on her desk.

"Let yourself be quieted" is a command in passive voice. While grammatically correct, it is also extremely convoluted, and sounds awkward.

"Let yourself be quietened" would be another British English variant, but no less awkward.

Be quiet : according to my point of view,this sentence will need verb to request to be into passive otherwise it won't change