I'm not 100% sure but I bet there is a density it can be compressed to fairly easily and then the ratio of pressure (or weight) to further compression will get increasingly steep. And the place at where it started getting steeper will depend on the type of wood - balsa being very different to, say, oak.
For a thick block of hardwood I'm sure you would need
FAR more that 1000 tonnes to flatten it - like as in millions or billions of tonnes, or maybe 1000 tonnes per mm^2. But even then its not going to disapear completely and so the weight will still be "above the floor". It would take something like a sugar cube sized block of a neutron star to flatten it completely!