Rope that wraps around sphere

Hello guys, i'd like to replicate this kind of functionality inside unity:

http://www.kanogames.com/play/game/wrrrmz (Please see level 2)

You see how this worm wraps around sphere and stretches while following mouse? I have tried making this using generated rope with mixed Hinje joints and Distance joints, but it does't work as in example.

As i am thinking there is no need of joints and rigid bodies, it can be achieved differently.

do you have any suggestions?