How chaperones interact with protein chains to assist in their folding is a central open question in biology. Obtaining atomistic insight is challenging in particular, given the transient nature of the chaperone-substrate complexes and the large system sizes. Recent single-molecule experiments have shown that the chaperone Trigger Factor (TF) not only binds unfolded protein chains, but can also guide protein chains to their native state by interacting with partially folded structures. Here, we used all-atom MD simulations to provide atomistic insights into how Trigger Factor achieves this chaperone function. Our results indicate a crucial role for the tips of the finger-like appendages of TF in the early interactions with both unfolded chains and partially folded structures. Unfolded chains are kinetically trapped when bound to TF, which suppresses the formation of transient, non-native end-to-end contacts. Mechanical flexibility allows TF to hold partially folded structures with two tips (in a pinching configuration), and to stabilize them by wrapping around its appendages. This encapsulation mechanism is distinct from that of chaperones such as GroEL, and allows folded structures of diverse size and composition to be protected from aggregation and misfolding interactions. The results suggest that an ATP cycle is not required to enable both encapsulation and liberation.