The Proto-Indo-European root *bʰedʰ- "to dig" in its o-grade form *bʰodʰ- became Proto-Germanic *ƀađjam "garden plot, sleeping place", then English bed. Finnish patja "cushion, bolster" is a borrowing of *ƀađjam.
In Latin, *bʰodʰ- became fodere, fossus "to dig", and fossilis "dug up", giving us fossil thru French.
The above is from the AHD. Unfortunately, the Oxford Dictionary of English Etymology is sceptical of this cool connection; saying about bed:
The ult. origin and primary sense are uncertain ; the Germ. base has been referred to IE. *bhodh-, as in L. fodere dig, fossa grave, ditch ; but uncertainty as to the priority of the chief Germ. sense, 'sleeping-place' and 'growing-paces for plants', invalidates conjecture
But it certainly wouldn't be the largest semantic drift we've seen.