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As is a conjunction, and is usually followed by a noun or pronoun in the nominative case. Like isn't a conjunction, but an adjective which behaves like a preposition being followed by a noun or pronoun in the objective case.
Afraid isn't a verb but an adjective, and we generally use it with the verb to be.
Here, rest is a noun, and we can't use it as an adjective in the meaning of what's left.