  We study optimal stopping of Feller-Markov processes to maximise an
undiscounted functional consisting of running and terminal rewards. In a
finite-time horizon setting, we extend classical results to unbounded rewards.
In infinite horizon, we resort to ergodic structure of the underlying process.
When the running reward is mildly penalising for delaying stopping (i.e., its
expectation under the invariant measure is negative), we show that an optimal
stopping time exists and is given in a standard form as the time of first
entrance to a closed set. This paper generalises Palczewski, Stettner (2014),
Stoch Proc Appl 124(12) 3887-3920, by relaxing boundedness of rewards.
