Wiki defines terminal object as the object towards which there is a single morphism from every other object of the category https://en.wikipedia.org/wiki/Initial_and_terminal_objects This definition is saying nothing about the possibility to have morphism from terminal object towards other object and how to interpret such morphism.
I have always thought that there are no morphisms from the terminal object, but, indeed, definition does not prohibit such morphisms.
There are use of such outgoing morphisms from the terminal object in the definition of fibrated categories and fibrations, see nice explanation in https://bartoszmilewski.com/2019/10/09/fibrations-cleavages-and-lenses/ where it is said that morphism from the terminal object into other object does the "selection of one element" (!) from this target object if it can be considered as a set of elements.
Is such interpretation true? How it is possible that terminal object have outgoing morphisms, what are their meaning and what are their application. Do such morphisms play the "selector" role indeed for the target object? Just trying to understand the notion of terminal object and why and where it is used?