CARACAS, Venezuela—Teresa Aray hunkered down in her car at nightfall recently, one of hundreds of motorists waiting for gasoline in a mileslong line in the eastern city of Puerto Ordaz.

Ms. Aray had locked her doors and hidden her cellphone and keys. She was barely able to sleep, fearing rampant street crime. Other drivers gripped rocks and pipes for protection, in one further indication that Venezuela, once a great oil power, has descended into chaos.

Despite...