べからず / べからざる

べからず means "must not", "do not": a flat prohibition, the language of signs, rules and old sayings. It follows the dictionary form of a verb. It is classical Japanese – the negative of べし – and it sounds stern and impersonal, as if the rule applies to everyone.

With する, the verb is classical す: ゆだん油断すべからず, いんしょく飲食すべからず. You will see するべからず on modern signs too, but すべからず is the standard form.

べからざる before a noun

べからざる is the form that goes before a noun: "that must not be…". It turns up in formal writing rather than on signs, mostly with a handful of verbs.

かく欠くべからざる is a set phrase, "indispensable": something you must not be without.

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Neither form belongs in conversation. To tell someone not to do something, say てはいけない or ないでください; for "indispensable", say かかせない欠かせない.