What happens when a subarachnoid cyst bursts due to head injury? is it always life-threatening?

It depends on many things- size location other illnesses. It is serious but not always life threatining if diagnosed early and treated

Would anticipate if a head injury were severe enough to rupture a subarachnoid cyst, the force would be sufficient to be life-threatening. But the usual closed head injury would neither cause such a rupture nor end in death. It is unusual for subarachnoid cysts to cause any clinical symptoms.