There exist a material that becomes permanently conductive after being exposed to light?
I'd say that depends heavily on the light. Especially on the heat that is deposited in your material. The keyword here is resistive switching (for example in oxides).
With light that deposits enough energy it is for example possible to switch phase change materials between a low and high conductive state. This is how DVDs work. For DVDs the reflectivity is read out, which also changes from one state to the other. But the resistivity is switched too, as you can see in the graph below.