By finding traces of past liquid water on Mars that was reasonably neutral, Curiosity has fulfilled its main mission. It has shown that an environment suitable for life as we know it once existed on the Red Planet.
That is but a step away from finding traces of ancient life on Mars. Curiosity is situated on the floor of what appears to have been a giant crater lake, eons ago. A very good place to be looking for fossils.
Living things (if any once exited there) would have sunk into the sediments on the lake floor. As conditions on Mars became harsher and harsher, and the lake dried up, the sediments hardened into stone, preserving the mineralized forms of whatever ancient life may lie there.