The discovery in deep near-infrared surveys of a population of massive quiescent galaxies at z > 3 has given rise to the question of how they came to be quenched so early in the history of the universe. Measuring their molecular gas properties can distinguish between physical processes where they stop forming stars due to a lack of fuel versus those where the star formation efficiency is reduced and the gas is retained. We conducted Atacama Large Millimeter/submillimeter Array observations of four quiescent galaxies at z = 3.5-4.0 found by the Fourstar Galaxy Evolution Survey and a serendipitous optically dark galaxy at z = 3.71. We aim to investigate the presence of dust-obscured star formation and their gas content by observing the dust continuum emission at Band 7 and the atomic carbon [C i]((3) P (1)-(3) P (0)) line at 492.16 GHz. Among the four quiescent galaxies, only one source is detected in the dust continuum at lambda (obs) = 870 mu m. The submillimeter observations confirm their passive nature, and all of them are located more than four times below the main sequence of star-forming galaxies at z = 3.7. None of the targets are detected in [C i], constraining their gas-mass fractions to be z = 3.7. These results support scenarios where massive galaxies at z = 3.5-4.0 quench by consuming/expelling all the gas rather than by reducing the efficiency of the conversion of their gas into stars.