Tabu search and simulated annealing don't suffer from this, because they always find acceptable move(s) sooner or later (TS because it accepts anything that isn't tabu and SA because every move has a change of being acceptable no matter what).

Late acceptance or great deluge with a moveSelector that is neverEnding (or too big to be called ending), will result in a never ending Solver because the Termination isn't checked in the move iterator (which it should... even if that results in a performance cost ).