Voltage drop problem with my solid state relay
More than likely what you are seeing is the leakiness of the SSR when it is switched off. Lets say you meter has 10 Mohm input impedance - the 80V implies a current of 8 uA which in turn implies the SSR has an open-circuit impedance of 35 v / 8 uA = 4.38 Mohms.

Else, the SSR is broken!