Actually, they would put a coin in or on a dead person's mouth,
to allow them to pay the ferryman Charon to take them across the river Styx
to Hades.
He is the God of the dead and Lord of the Underworld.
gold drachmas
That the dead could not come back in a physical body.
Much as we do today in preying, it was because we all die and mourn those who die and so they preyed to the god of the dead.
Ancient Greeks often attempted to speak to the dead who knew all things in the past and future: Odysseus did this for advice.