I have friends that have applied silicone caulk on the reverse side of their runner rugs along the edges.... (they let it dry for about 12 hours before using) They do wash them, don't know if they put their rugs in the dryer, though.
If in doubt as to any chemical reaction from the caulking having prolonged contact with the material of the floor , I'd try good old fashioned double sided carpet tape on a rug without a non skid backing. Might be a pain at times, but safer as to chemical reaction.
Keep in mind that direct sunlight can be a contributing factor in any color change of the floor, if part of the floor is exposed to the sun and part is continually covered, no matter what the rug backing is.
