I need a line to be grounded as power to a board is failing. Complicating the issue is the fact that this line is critical to circuit operation and cannot tolerate even nanoVolts of additional noise when working properly. Typical frequencies are less than 1kHz, the voltage can be up to +/-10V driven from a 10K output impedance

It's the +/- input to a highly sensitive analog PID loop. When the input is exactly 0V it thinks everything is fine and perfect. As the power fails, it goes mad and swings wildly and unpredictably. By grounding that input the PID will think all is well even as it dies.

The ugly mechanical way to do it is use a normally closed mechanical relay that is held open by the PSU. When the latter fails the closed relay shorts the line to analog ground before the power to everything else drops below the working voltage.

Under normal working conditions nothing is connected to the input line from this relay (except a short stub of track)

Is there a way to do it using non-mechanical means?