There is a cloth material that is non-combustanble material that when placed on the floor beneath the area where a person is soldering will prevent a spark from starting a fire.  I don't think it is wool but it is a common material that can be bought in a store.  What I read a long time ago is to wet the material and place it on the floor where you are going to solder.  My problem is that where I am going to solder has a wall to wall rug--so I have to be careful.  Anyone know of the material?

It would be a lot better if you could find a place that didn't have carpet to solder but since you seem to have no choice I suggest that you visit a welding supply store and get a welding blanket. These are fire resistant sheets that are placed over or around objects that need to be protected from sparks from welding torches.

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You could try something like fire board, it's the stuff you can find in a home improvement store to put on the walls surrounding a stove in your house. Something like that, or even around a wood stove on the walls. Or the layer between the brick on a fireplace and the sheet rock of the walls.