Case means some kind of dielectric enclosure, quite common for a PCB antenna, I think. Definitely not a conducting cage.
It's not clear to me, what efficiency in your simulation means. Does it refer to antenna impedance mismatch or losses inside the antenna? Or is it just an simulation artefact indicating insufficient accuracy? If you see efficiency < 1, a correct simulation should tell you where the energy is gone.
In the first case, you should primarly adjust the impedance matching.
Placing dielectric media near the antenna will affect both antenna directivity and impedance matching. If the latter hasn't be optimal before, it can be improved, otherwise get worse.