  We derive universal bounds for the finite-time survival probability of the
stochastic work extracted in steady-state heat engines and the stochastic heat
dissipated to the environment. We also find estimates for the time-dependent
thresholds that these quantities does not surpass with a prescribed
probability. At long times, the tightest thresholds are proportional to the
large deviation functions of stochastic entropy production. Our results entail
an extension of martingale theory for entropy production, for which we derive
universal inequalities involving its maximum and minimum statistics that are
valid for generic Markovian dynamics in non-equilibrium stationary states. We
test our main results with numerical simulations of a stochastic photoelectric
device.
