Kinetic theories of crystallization of polymers do not apply to high supercooling. The thickness of the crystalline lamellae becomes independent of the crystallization temperature and is a characteristic parameter of the polymer. We relate this limiting thickness to the flexibility of the polymer chain in the pure liquid or in solution before crystallization. The folded chain in the crystalline state is analogous to the coiled chain before crystallization. Flexibility and limiting thickness depend in a similar way on the solvent, defect concentration in the polymer chains, pressure, pH, and salt concentration in case of crystallization of polyelectrolytes. Folded chains appear also in oligomer crystals when the oligomers have a coiled shape in the liquid state. The limiting fold period of crystalline polymers and oligomers is found to be an order of magnitude greater than the persistence length of the Gaussian chain in the liquid state.