On 11 and 12 May 1999, the Earth was engulfed by an unusually low-density (<1 cm-3) and low-velocity (<350 km s-1) solar wind for a period of over 1 day. Extensive studies of this unusual event that occurred during Carrington rotation 1949 (CR1949), using both ground-based and space-based in situ observations, have not as yet been able to identify the cause or the solar source of this event. Using solar wind velocity measurements from the four-station IPS observatory of the Solar-Terrestrial Environment Laboratory (STEL), Toyokawa, Japan, we investigate the structure of the solar wind in May 1999 during CR1949. IPS observations from STEL were used to make tomographic velocity maps to identify and delineate the extent and morphology of the stable solar wind flows during CR1949 in the vicinity of the Earth. Combined with in situ measurements of the interplanetary magnetic field (IMF), potential field computations of the solar magnetic fields in the period, and HeI 10830¿ observations of coronal hole boundaries during CR1949, we have identified the source region of the unusual flows and have shown that the flow responsible for the disappearance event was a stable unipolar flow originating in the vicinity of a large midlatitude active region AR8525, located at ~18¿N and between heliographic longitudes 280¿ and 300¿. Earlier workers have speculated that such events may be caused by the large-scale restructuring of the solar magnetic field at the maximum of each solar cycle. However, by identifying the solar source and nature of this event, we believe that at least in this particular case, the association with global, large-scale solar phenomena like the periodic 11-year solar polar field reversal is most likely to be coincidental.