There is very little danger with floor tile because any fiber is encapsulated in an asphalt or vinyl matrix. You can safely remove the loose floor tiles and discard them. If the floor is generally loose, try removing all of it using a wetting solution and a floor scraper. Just avoid excessive breakage, seal the tiles in plastic disposal bags and check with your disposal company on any other requirements. Most floor tile removed by the residential owner is not regulated. You can then recover the floor in a sheet product.

Another alternative may be to cover over the existing tile. The most appropriate choice will depend on whether you have moisture issues on the floor or not.