Most science fiction plots rely on a physical device to establish this region.
Storylines using such fields often have materials as well as living beings surviving thousands or millions of years beyond their normal lifetimes.
One use of stasis fields is as a form of suspended animation: to let passengers and cargoes (normally of spacecraft or sleeper ships) avoid having to experience extremely long periods of time by "skipping over" large sections of it.
There are real phenomena that cause time dilation similar that of a stasis field.
Extremely high velocities approaching light speed or immensely powerful gravitational fields such as those existing near the event horizons of black holes will cause time to progress more slowly.