Has anyone gone through asbsetos removal during the purchase of a home?

I agree with Bare B above. Leaving the floor becomes a disclosure issue for you once you decide to sell. That may put you in the position of having to pay to remove it anyways to sell the house. In addition, the tiles are not a danger as long as they do not disintegrate or begin to degrade. How can you guarantee that once you cover them with carpeting the moisture from having the carpets cleaned, the pressure from moving furniture or dropping things won't create a very big problem of them deteriorating right under your feet without your knowledge? You may not even be able to find an insurer to give you homeowners insurance without exclusions. Run, do not walk away from this deal unless the bank is prepared to take total financial responsibility for this risk.