With a uniform ideal rope, in an ideal container that is only as wide as the thickness of the rope and no friction between the rope and the inner wall of the container. The container is bottomless and the rest of the rope is rested on the table right below the container. That is, an ideal rope (say, sufficiently long) going through an ideal tube of a finite length.
In this setting, intuitively, I am guessing the rope will arch as the pull of gravity increases since the pull mainly just needs to overcome the mass inertia of the portion of rope in the tube plus the length that makes the arch and the portion between the bottom of the tube and the surface of the table. To see this, we only need to imagine the portion of the rope being pulled down by gravity being indefinitely long.
