Connect the pushbutton to drive a relay coil. Then connect the relay's NC and common primary contacts where you would normally connect the NO push button terminals. Note that the relay coil will always consume power when not pushed though...The idle current will be whatever the relay's coil current is which could be some tens of milliamps.
simulate this ...
here you can see a printed force sensor
the black rectangle is a film resistor and the black conductive rubber dome bridges it progressivly. the harder you press the more conductivity the dome contributes and the lower the measured resistance is.
image from here:
How do Dualshock 4 pressure sensitive buttons work?