A little history:
"crever" means to die in popular speech.
In Old and Middle French, la dalle referred to a stone slab, such as: the slab in front of a house or shop.
These spots were frequently where beggars sat or lay, because it was a visible place where they could ask for charity.
So, being “on the slab” meant being in the street, exposed, poor, and without shelter.
It was a reference to the miserable death of someone too poor or too hungry to survive.