Rubber backing is great to keep scatter rugs in place, but rubber breaks down over time. It is susceptible to damage from chemicals and heat present in the wash and dry cycles of modern appliances, the constant wrinkling and smoothing from foot traffic, and even exposure to ultraviolet light indoors and out. The tops of rugs generally last much longer than the backing, though, so if you are not ready to throw out the rug, simply repairing the backing will give the rug many more years of use.
Wash and rinse the rug using as little detergent as possible to get it clean. Do not use fabric softener or other additives in either the wash or rinse cycles. Hang the rug to dry.
Lay the rug upside down on a stable, flat surface where it can remain for at least 24 hours undisturbed. (The room should be warm--at least 65 degrees F--for the latex rubber to cure properly.)
Brush or cut away any scraps of old backing, string, etc., from the rug so the surface is as smooth as possible.
Open a can of liquid latex rubber and stir carefully to mix contents that may have settled.
Dip a brush into the liquid latex, and apply a generous coat to worn areas of the backing to consolidate any flakes and cracked areas. If whole areas of backing are loose but still attached, coat the area beneath the damaged portion with a thin coat of latex and press the old backing down over it. (The latex acts as a glue.) Allow the latex to cure for several hours (until it is solid and not sticky).
Apply an additional coat of liquid latex over the entire back of the rug to make a single, uniform surface over repaired areas. Allow to cure as before--preferably 24 hours before using.