upon where you live and the laws governing real estate transfers in your area. In Illinois, there are requirements for disclosure of defects and hazards, such as asbestos, if they are known to the sellers. It is possible that the people who sold you the house did not know what type of flooring it was. If they never dug it up the way you did, and whoever sold it to them didn't tell them, they may not have been aware of it.
I'm wondering about your home inspection. Why didn't this get discovered during the inspection? Surely this odor was there before you moved in, given the advanced state of decay of the floor. Did you use someone who is insured? If so, you may have some recourse through the inspection company for their negligence in failing to discover this and inform you of it prior to the purchase. Get out your contract with the inspection company and examine it for warranty/guarantee language. There will probably be some liability-limiting language as well (some limit their liability to the amount that you paid for the inspection), so watch for that.
On the other hand, when the removal company comes out, you may learn that this is not asbestos after all, which would be excellent news. Good Luck.