We present ultradeep radio observations with the Expanded Very Large Array of 4U 1957+11, a Galactic black hole (BH) candidate X-ray binary known to exist in a persistent soft X-ray state. We derive a stringent upper limit of 11.4 μJy beam-1 (3σ) at 5-7 GHz, which provides the most rigorous upper limit to date on the presence of jets in a soft state BH X-ray binary (BHXB). X-ray, UV, and optical fluxes obtained within a few weeks of the radio data can be explained by thermal emission from the disk. At this X-ray luminosity, a hard state BHXB that follows the established empirical radio-X-ray correlation would be at least 330-810 times brighter at radio frequencies, depending on the distance to 4U 1957+11. This jet quenching of >2.5 orders of magnitude is greater than some models predict and implies that the jets are prevented from being launched altogether in the soft state. 4U 1957+11 is also more than one order of magnitude fainter than the faintest of the "radio-quiet" population of hard state BHs. In addition, we show that, on average, soft state stellar-mass BHs probably have fainter jets than most active galactic nuclei in a state equivalent to the soft state. These results have implications for the conditions required for powerful, relativistic jets to form and provide a new empirical constraint for time- and accretion mode-dependent jet models, furthering our understanding of jet production and accretion onto BHs.