Quantum trajectories are crucial to understanding the evolution of open systems. We consider an open cavity mode undergoing up and down multistate quantum jumps due to the emission and absorption of photons. We prove that among all subtrajectories, starting simultaneously from different photon number states, only one survives a long single-run evolution. A random Fock state terminating the subtrajectory becomes known for the ergodic case via the key-the processed record of the input and output photocounts, and the trajectory duration. Based on this result, we propose a robust protocol to infer the Fock state, a valuable resource for quantum applications.
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