We obtained deep imaging and high-resolution spectroscopy of the planetary nebula NGC 2438. In addition to the bright inner rim and the faint halo-like shell already known from previous imagery, our observations also highlight the existence of an even fainter large halo of nearly spherical shape. Analysis of the surface-brightness profiles and the line splitting indicates a clear ionization stratification within the bright rim, with the flow velocities increasing with distance from the central star, reaching 37 km s-1. We compared the surface-brightness profiles and kinematical data of NGC 2438 with state-of-the-art radiation-hydrodynamics models, and obtained a surprisingly good qualitative agreement. By means of this modelling we show that the faint, halo-like shell has formed by recombination from a once well-developed photoionized shell in response to a fast luminosity drop of the central star. The large, very faint halo is interpreted as being the relic of the now fully ionized AGB wind. Also the velocity/ionization stratification and the thickness of the bright rim are fully consistent with the prediction of the models for such an evolved planetary nebula. The properties of NGC 2438 can be explained by assuming that the planetary nebula formation started about 45 000 years after a thermal pulse on the AGB, and that the remnant star continued to burn hydrogen in a shell until burning has stopped quite recently. Based on observations obtained at the 3.5m~NTT telescope of the European Southern Observatory