Unitary death of Schr\"odinger's cat

We analyze dynamics of the Rabi model describing interactions of a qubit with a single soft-mode oscillator. We show that the model with a slightly violated parity generates symmetric Schr{\"o}dinger cat states of the oscillator, which suddenly perish in a spontaneous unitary process similar to the measurement-induced wave-function collapse. The effect is sufficiently robust to be tested experimentally, e.g., with trapped ions, macroscopic mechanical oscillators or superconducting circuits.