Chaperonins assist folding of many cellular proteins, including essential proteins for cell viability. However, it remains unclear how chaperonin-assisted folding is different from spontaneous folding. Chaperonin GroEL/GroES facilitates folding of denatured protein encapsulated in its central cage but the denatured protein often escapes from the cage to the outside during reaction. Here, we show evidence that the in-cage-folding and the escape occur diverging from the same intermediate complex in which polypeptide is tethered loosely to the cage and partly protrudes out of the cage. Furthermore, denatured proteins in the chaperonin cage start their folding from extended conformations but not from compact conformations as usually observed in spontaneous folding. We propose that the formation of tethered intermediate of polypeptide is necessary to prevent polypeptide collapse at the expense of polypeptide escape. The tethering of polypeptide would allow freely mobile portions of tethered polypeptide to fold segmentally. The folding acceleration and deceleration by chaperonin for various substrate proteins can be explained by considering the tethering.