Story Telling

This is a venerable literary tradition:

two or more characters relax in comfortable surroundings;
one of the characters recounts an adventure that he has had;
what he recounts becomes the main story that we are reading;
we return to the comfortable surroundings at the end of the story.

(In fact, this is how stories were told before they were written down.)

Examples:

in Virgil's Aeneid, Aeneas reaches Troy in Chapter One, then spends Chapter Two recounting the sack of Troy and Chapter Three describing his travels;

in Chaucer's The Canterbury's Tales, pilgrims exchange stories in an inn;

in HG Wells' The Time Machine, the Time Traveler describes his temporal journey to his dinner guests;

in Neil Gaiman's The Sandman: Worlds' End, the Chaucerian scenario is repeated in an inter-universal inn;

in two of Poul Anderson's Nicholas van Rijn stories, van Rijn's employees tell him of their experiences on other planets.

Observations
(i) Usually, the survival of a first person narrator is guaranteed by the fact that he is able to narrate. All the more so when we have seen him sitting comfortably before he begins.
(ii) There can be both an outer and an inner narrator, as in The Time Machine and in Anderson's "The Master Key."
(iii) The author, and the outer narrator if appropriate, must make the comfortable surroundings seem as real as the setting(s) of the main story.

In Anderson's "Esau" and "The Master Key":

the narrations occur in van Rijn's penthouse on the Winged Cross in Chicago Integrate;
this setting is fully realized;
there is plenty of conversation before and after the main narration;
thus, we appreciate both the dangers encountered by van Rijn's employees and the comfortable surroundings in which they later relax.