As long as the center of gravity of the length of beads outside the jar is below the surface of the remaining string inside the jar, the gravitational force down on the length outside the jar will be greater than the gravitational potential to overcome lifting the string from inside the jar.
why does it lift?
I am going to say "lateral acceleration".
A body in motion tends to stay in motion. Any change in direction is lateral acceleration.
For every action there is an equal and opposite reaction.
As the direction of motion of the chain is changed from horizontal to vertical, there is an equal force directing the chain to continue horizontally as there is to accelerate it downward.
That apposing force eventually lifts a section of the chain.
Prediction: Barring any resistance, the faster the chain falls, the higher the arc.
It reminds me of setting siphon tubes to irrigate 40 acres of corn.
