This is a screenshot that I took from Gmod, after modeling this scene.
Rouge got elastic superpowers after falling into a vat of non-lethal or carcinogenic chemicals tank, somewhere in Chemical Plant Zone.
Her joints, muscles and bones are in a more elastic state.
She uses that powers for useful things such as catching bad guys and get an emerald instead of the trapped thief.
She catches Fang the Sniper at Casino Park and catches the emerald that she dreams to have.