We report extensive interplanetary scintillation (IPS) observations of the solar wind during the period centered around 11 May 1999, when the Earth was engulfed by a region of solar wind with unusually low densities (<1 cm-3) and velocities (<350 km s-1). IPS observations with the Ooty Radio Telescope (ORT), operating at 327 MHz, probe the inner heliosphere along a large number of closely spaced lines of sight over the heliocentric distance range of 0.2 to 1.0 AU, daily, at the rate of about 150 sources in the course of 10 hours. Using these observations, the southern half of the inner heliosphere was monitored everyday between 3 and 16 May 1999. The data show that the solar wind densities were globally subdued, having started subsiding from 3 May 1999, itself at different parts of the heliosphere. This was accompanied by a noticeable decrease in the velocity of the general solar wind also. The IPS data also reveal a small subset of closely spaced sources lying to the west of the Sun that show a steep drop in inferred densities to immeasurably low amounts on and around the 11th May. The actual morphology of the subsidence event, from our observations, is shown to be that of a void-within-a-void. The role of the polar magnetic field reversal that was taking place between Carrington rotations 1947--1954, which may have played a key role in generating the subsidence event, is also examined. To the best of our knowledge this is the first time that sustained levels of low densities and velocities have been recorded for such a long period over a large part of the inner heliosphere. Some possible signatures of high energy strahl electrons were also recorded in this period.