We study two-photon excitation of Rydberg states of atoms under stimulated adiabatic passage with delayed laser pulses. We find that the combination of strong interaction between the atoms in Rydberg state and the spontaneous decay of the intermediate exited atomic state leads to the Rydberg excitation of precisely one atom within the atomic ensemble. The quantum Zeno effect offers a lucid interpretation of this result: the Rydberg blocked atoms repetitively scattering photons effectively monitor a randomly excited atom which therefore remains in the Rydberg state. This system can be used for deterministic creation and, possibly, extraction of Rydberg atoms or ions one at a time. The sympathetic monitoring via decay of ancilla particles may find wider applications for state preparation and probing of interactions in dissipative many-body systems.