  We present extremely deep upper limits on the radio emission from 4U~1957+11,
an X-ray binary that is generally believed to be a persistently accreting black
hole that is almost always in the soft state. We discuss a more comprehensive
search for Type I bursts than in past work, revealing a stringent upper limit
on the burst rate, bolstering the case for a black hole accretor. The lack of
detection of this source at the 1.07 $\mu$Jy/beam noise level indicates jet
suppression that is stronger than expected even in the most extreme thin disk
models for radio jet production -- the radio power here is 1500--3700 times
lower than the extrapolation of the hard state radio/X-ray correlation, with
the uncertainties depending primarily on the poorly constrained source
distance. We also discuss the location and velocity of the source and show that
it must have either formed in the halo or with a strong asymmetric natal kick.
