Last week I was asked by an experienced alarm tech on how he could get a door alarm to stay on until reset if a fire door was opened. He had thought about various modules like timer boards etc, but obviously, they time out and are relatively expensive.
The easiest way to achieve this is to use a latching relay. To do this you need a relay with 2 sets of contacts. You use one set of contacts to drive your external device, and the other to cause the relay to latch on when energised. The basic circuit is as follows:
When the input (eg N/O reed switch on the door) is triggered the relay energises, which causes relay contact 1 to go to the closed state. As relay contact 1 is in parallel with the trigger input it is permanently closed until power is removed from the relay.
Relay contact 2 is of course a dry (voltage free) contact and may be used for any external device you may require.