  We analyze the open dynamics of quantum systems conditioned on no jumps being
detected. We first obtain general results relating the no-jump probability and
the waiting-time distributions to the conditional evolution of specific system
observables. These results are applied to single-qubit models, whose
conditional dynamics is quite involved and shows a rich set of physical
behaviors. Furthermore, we obtain general expressions for the no-jump dynamics
of non-interacting fermionic-bosonic chains undergoing Gaussian-preserving
dynamics. We show that the conditional dynamics is determined by a non-linear
Riccati-type differential equation for the correlation matrix. Finally, we
apply our results to chains of hopping particles under inhomogeneous jump rates
and boundary driven systems in presence of pairing terms.
