1. There are a couple of tried and tested methods that hold floor rugs in place on solid floors:
a) a thick underlay just slightly smaller than the rug, so that the edges of the rug tough the floor surface- felted wool is my preferred option but cotton and wool mixes work well, I’m just not so keen on a solid surface of rubber or plastic.
b) open mesh of rubber, fibre rubber mix or some sort of synthetic, does a good job, as the carpet naturally beds itself into it, and the grid construction that remains free is naturally resistant to slippage. Sometimes these mats seem to have a sticky sort of finish that may be OK, but can pull the polish or finish away from the surface beneath.
2. In the construction side of furnishings, as with tailoring and couture, interfacings need to hold to the layers of fabric on either side: here the weave constructions help – slightly nubbly sides or a fairly coarse weave encourages them to hold, to bed into the fabric, until they are further held in in place with specialist stitching.
3. Pile fabrics and slippery fabrics can extremely difficult to seam; the trick is to place another material between- fine tissue paper or a vanishing cloth – to limit the slip or walk. Once the seam is stitched, the papers can be carefully torn away or the vanishing cloth washed out.