It is a complete sentence. "It" (whatever it is) is coupled with the nightmare of drugs and crime, which has made it worse. The main clause is "It has got worse", which has a subject ("it") and a predicate (a verb and the rest of the clause); the segment at the beginning is a modifier and does not need a complete verb phrase.
The sentence is complete in the strict traditional sense (subject and predicate with a full verb are present); but whether it makes sense depends on what "it" is, which depends on the context the sentence is in.
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