Initially, the configuration shown is unstable. The negative charges repel each other. If there is any slight rotation of one of the rods, the repulsion can result in further rotation away from this configuration. There are three possible final configurations as shown below.
Configuration (A) is stable. If the positive upper ends of both the rods are pushed towards each other, then their mutual repulsion will move the system back to the original configuration. Configuration (B) is an equilibrium configuration, but it is unstable. If the lower ends of both the rods are moved towards each other, then their mutual attraction will be larger than that of the upper ends and thus, the configuration will shift to (c), another possible stable configuration.