This is largely a mental exercise and probably not original. I would never use such a circuit except in an emergency or maybe a proto-prototype if a delay-off relay wasn't available. If a delay-off relay was needed in a design, that's what would be specified. However, I recently received a batch of nice delay-on relays and wondered if there was a way they could be used as delay-off relays. Because they are double throw relays, it's possible with the addition of a regular (aka instant or no-delay) DPDT relay. And to be safe in most situations, a SPST-NO relay would be needed too.
The basic design is pictured below. Some items that would normally be used, like coil TVS devices, have been omitted. The circuit is shown with electromechanical relays, but would work with SSRs.
To see how it would work, we'll step through use of the control switch.
1. Imagine the control switch is open and has been for at least the delay time of the delay relay. The instant relay coil is not activated, so there will be no power to the load via the instant relay. However, there will be signal power from the instant relay to the coil of the delay relay, so there will also be no power to the load via the delay relay.
2. Now imagine the control switch is closed. The coil of the instant relay will be activated and the instant relay will send power to the load and stop sending signal power to the delay relay. Because the delay relay is no longer be receiving signal power, its coil will be deactivated and it will also start sending power to the load.
3. Next imagine the control switch is opened. The coil of the instant relay is deactivated, and it will no longer be sending power to the load. However, the instant relay is now sending signal power to the delay relay. The delay relay will continue to send power to the load until the delay time has expired, at which point, its coil will be activated and power will no longer be sent to the load.
If unplanned power to the load would be harmful (often the case), then the safety relay should be used. Without the safety relay, if the signal power source fails, but the load power supply is active, then the load would be energized. The safety relay eliminates this scenario. No safety relay would be needed if signal and load use the same power source.
This circuit has disadvantages compared to a single delay-off relay:
a. more complex; so, more ways to fail.
b. more expensive in most cases.
c. requires more space.
d. at least one relay will always be powered.