"I think, generally speaking, it's not the greatest career move. Personally, I would rather not be famous than dead." - Ben Affleck, on actors who contemplate suicide in pursuit of fame

While the meaning of Ben's statement is clear, the structure of the second sentence is not grammatically correct.

The components of this sentence are a subject ("I"), a linking verb (the helping verb "would" and "be"), an adverb ("rather"), and a compound predicate adjective (the adjectives "not famous" and "dead" joined by the conjunction "than"). The problem is the placement of the second part of the verb ("be") between the two components of the first adjective ("not famous"). The structure of the sentence would be more logical if "be" were placed after "rather." Syntax featuring an adverb between two parts of a verb is both common and grammatically correct.

I would rather be not famous than dead.

The statement would be more concise if "not famous" were to be replaced with a one-word synonym.

I would rather be unknown than dead.