The stellar content, structure and evolution of the extreme low-luminosity Sculptor dwarf irregular galaxy (SDIG) have been studied using optical (B, R and H alpha) and near-infrared (J and K) imaging at the Anglo-Australian Telescope (AAT). Despite the presence of many blue stars, there are at present no detectable H II regions, indicating that the galaxy is now in a relatively quiescent state. However, the ratio of the H I mass to blue luminosity is typical of other late-type galaxies, suggesting that SDIG has faded by less than a magnitude in B since it stopped forming stars, Highly luminous red stars have been discovered, which appear to be members of an asymptotic giant population at least similar to 6 Gyr old. Thus, stars had already formed in SDIG long before the most recent burst, Optical surface brightness profiles of SDIG closely follow an exponential law, as is observed for other dwarf irregular galaxies, The central surface brightness is comparable to that of dwarf spheroidals of the same luminosity. Since the fading track follows the dwarf spheroidal sequence, it is not possible to rule out SDIG-like galaxies as progenitors of dwarf spheroidals on photometric grounds alone. SDIG ranks among the least luminous dwarf irregular galaxies, and by inference should have an oxygen abundance comparable to that of IZw18, To reconcile the low metallicity with the rather high stellar mass fraction, however, either SDIG has lost a significant fraction of its gas, or past star formation has proceeded with an initial mass function which is steeper than is typical in more enriched dwarf irregulars.