We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method (PERM). The nanotube is a long channel opened at one end and its diameter D is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position x inside the tube: the free energy of confinement, the average end-to-end distance, the average number of segments imprisoned in the tube, and the average stretching of the confined part of the chain for various values of D and for the number of repeat units in the chain, N. We show that when the chain end is dragged by a certain critical distance x* into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and the average stretching parameter. The critical distance scales as x* similar to ND1-1/v. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes.