Context. From May 24-25, 2002, four spacecraft located in the solar wind at about 1 astronomical unit (au) measured plasma densities one to two orders of magnitude lower than usual. The density was so low that the flow became sub-Alfvénic for four hours, and the Alfvén Mach number was as low as 0.4. Consequently, the Earth lost its bow shock, and two long Alfvén wings were generated. Aims. This is one of the lowest density events ever recorded in the solar wind at 1 au, and the least documented one. Our goal is to understand what caused the very low density. Methods. Large Angle and Spectrometric Coronagraph (LASCO) and in situ data were used to identify whether something unusual occurred that could have generated such low densities Results. The very low density was recorded inside a large interplanetary coronal mass ejection (ICME), which displayed a long, linearly declining velocity profile, typical of expanding ICMEs. We deduce a normalised radial expansion rate of 1.6. Such a strong expansion, occurring over a long period of time, implies a radial size expansion growing with the distance from the Sun to the power 1.6. This can explain a two-orders-of-magnitude drop in plasma density. Data from LASCO and the Advanced Composition Explorer show that this over-expanding ICME was travelling in the wake of a previous ICME. Conclusions. The very low densities measured in the solar wind in May 2002 were caused by the over-expansion of a large ICME. This over-expansion was made possible because the ICME was travelling in a low-density and high-velocity environment present in the wake of another ICME coming from a nearby region on the Sun and ejected only three hours previously. Such conditions are very unusual, which explains why such very low densities are almost never observed.