No, not a final gradual ritardando. It's hard for me to describe. It may only be a thing in musical theater. Here are some examples:
This musical section is referred to colloquially as the "kick line." (see also The Rockettes)
It is characterized by 4/4 (or equivalent) meter, and a tempo drastically reduced from whatever came immediately prior, often accelerating gradually to eventually match that of what came before.
You're correct that it is specific to musical theatre; the name comes from the choreography that often accompanied it of a line of dancers doing unison kicks in time with the music.
It shows up at the end of songs because this choreography would often be used for a "big finish".
This name applies equally to the musical idiom as well as the dance idiom, even if the choreography is totally different (in the case of the Tony Awards clip) or not present at all (in the case of the West Side Story clip).
It could also be a fermata which means pause and is used to give a drawn out effect towards the end of pieces.
Another notation that could be what you need is a
corona (in english is
fermata). It is often used in final parts and allow the player to keep a note as long as he wants.
For more information see the wikipedia page