Reverse NC output to NO for a card reader
simulate this circuit &ndash; Schematic created using CircuitLab
Figure 1. What you've got, want and can have.
If the reader and solenoid are on the same supply then you don't need RLY1 as the lock can't open without a supply.
Figure 1c shows a workable solution:

RLY1 proves the reader power is OK. If power is lost then its contact opens as shown on the right and the UNLOCK3 solenoid cannot operate.
RLY2 will be normally energised so its contact on the UNLOCK3 circuit is normally open and UNLOCK3 is de-energised.
If RLY1 is on and the card-reader gets a valid card CR1 will open, RLY2 will turn off. Now RLY1's contact will be closed, RLY2's NC (normally closed) contact will close and UNLOCK3 will be energised to unlock the door.