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Add in a liquid diluent. Use a bar of clay softener. Add in liquid clay. Add mineral oil. Rub the clay with petroleum jelly. Combine hard clay with fresh clay.
A liquid diluent is one product on the market that softens unworkable clay. Many diluents are manufactured by the companies that make polymer clay, and they are made specifically for rejuvenating old clay.  Use liquid diluents if warming and kneading the clay doesn’t work to soften it. Add in liquid diluents a drop at a time as you knead the clay. Adding too much can make the clay mushy. Liquid diluents can be used as a glue, and therefore may add stickiness to your clay. If your clay is becoming too sticky, wrap it in a paper towel to absorb some of the stickiness. There are also several clay softeners that come in bar form. Instead of being liquids that you add, the bars are made of a neutral mixing compound that helps your clay become more workable.  Use one part of solid clay softener to five parts of clay. Warm the clay, then add the bar clay softener and knead until the clay and the clay softener are mixed. Bar clay softeners are whitish colored and therefore work best with highly saturated clay. Be aware that adding too high a ratio of bar clay softener can dilute the color of the clay. Liquid polymer clay is another material that can be used to make hard clay more pliable. Use liquid polymer in a similar way as you would the diluent, adding it drop by drop and kneading the clay in between drops until the clay has reached the right consistency.  Try to use uncolored liquid clay so that it doesn’t affect the color of the clay. You can also use tinted liquid clay, but it will slightly change the original color. Even though mineral oil is not made specifically for helping to soften clay, it does work wonders to soften and improve the texture of polymer clay. Add in a drop of mineral oil at a time, kneading in between each drop until the clay is workable. Petroleum jelly is a common household product that you can use if you don’t have access to commercial clay softeners. To use petroleum jelly, dab a small amount on your fingers and rub it into the clay. Then knead the clay to mix in the petroleum jelly. Keep adding more until you reach the optimal consistency. Another option that you have is to simply tack on fresh clay to the hardened clay, then knead the clays together. The more new clay that you add, the softer the combined clay becomes. Be sure to add clay of the same color unless you don’t mind the colors mixing. Knead the clay with your hands until the clay feels consistent throughout.