That expression comes from the days when people slept on beds filled with dried grass or hay.

VOA: special.2009.09.20

If a test finds that soil has too much lead, you might be advised to remove the soil or cover it with sod grass.

VOA: special.2009.06.09

Some people use grass cuttings or newspapers.

VOA: special.2009.06.30

There are no gravestones or grand mausoleums - just a patch of bare grass surrounded by a simple wooden fence.

VOA: standard.2010.07.22