1. Place a proxy on (x1, y1, z1) in a network
2. Bind a proxy card and put it in a screen in the same network: it will correctly output any variables in the top proxy slot.
3. Break the proxy with a wrench (shift+rightclick)

If you place that proxy on a position (x2, y2, z2) in the network where (x1, z1) == (x2, z2) then any values in the top proxy slot will correctly be shown on the screen.

If you however place the proxy on a position where (x2, z2) != (x1, z1), then the proxy will be unable to find the variable in the network.

Apparently it was independent of the (x,z) coordinates after all.
The problem was that the cable connections were saved into the item and not reset after placement.