Hi, BB. My guess is that the "cheesecloth" on your floor is actually the backing for the carpet pad and the foam rubber has just disintegrated from age, heat, perhaps water or pet urine or whatever leaving what you now find. Since you will be machine sanding with 24 or 36 grit paper, there is not much sense in spending a lot of time getting up the residue. You will want to vaccuum up any loose material just to cut down on the debris later on. I do have a hunch that you do have a water or pet urine problem but I hope not. If you find black stains in the wood, that is the problem.