Falling into bottomless pipe? Well, if it is bottomless, I believe, that it means it opens up in space.
In this case, anyone "falling" through such pipe can be considered to be separate space object, and dealt with exactly like any other space object, abuding to same physical laws.
In a particular case of falling through a tube going exactly through the center of planet...
Either, the "center" of gravity will be outside the pipe, in which case, one will fall on the wall of this pipe, closest to the gravity "center". Either, if "center" is within the pipe, falling object will be oscillating within pipe, until air friction, and bumps against the walls won`t stabilise it still within the "center".
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.