From the Super Mario Wiki
In Mario & Luigi: Partners in Time, the Shroobs were looking for a new place to live, as the planet they were living on was withering. During their search for a new home, they spotted the Mushroom Kingdom and invaded soon after. Mario, Luigi, Baby Mario, and Baby Luigi then defeated the Shroobs, however.
It is unknown if the Shroob Planet still exists; the prologue for Mario and Luigi: Partners in Time implies that the planet was withering and dying. This, along with the planet's Mushroom-like shape, suggests it is at least partially organic.
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