  We theoretically investigate the consequences of proximity-induced
conventional superconductivity in metals that break time-reversal and inversion
symmetries through their energy dispersion. We discover behaviors impossible in
an isolated superconductor such as an equilibrium supercurrent that apparently
violates a no-go theorem and, at suitable topological defects, non-conservation
of electric charge reminiscent of the chiral anomaly. The equilibrium
supercurrent is expected to be trainable by a helical electromagnetic field in
the normal state. Remarkably, if the band asymmetry exceeds the critical
current of the parent superconductor in appropriate units, we predict a perfect
superconducting diode effect with diode coefficient unity. We propose toroidal
metals such as UNi$_{4}$B and metals with directional scalar spin chiral order
as potential platforms.
