No, jaggery should not be stored with rice for moisture control. Jaggery attracts moisture, potentially damaging both the jaggery and the rice.
Jaggery, being a natural sweetener, is hygroscopic, meaning it readily absorbs moisture from the surrounding air. Storing it with rice, which is typically kept in a dry environment to prevent spoilage, would introduce moisture to the rice. This can lead to mold growth, insect infestation, and a general degradation of the rice quality. Furthermore, the jaggery itself would become sticky and potentially dissolve or ferment due to the absorbed moisture, rendering it unusable. It's best to store jaggery in an airtight container in a cool, dry place, separate from other food items that require a dry environment. Rice should also be stored in an airtight container, but with desiccants if necessary, not with moisture-attracting substances.
If your jaggery becomes hard, don't throw it away! You can soften it by placing it in a microwave-safe bowl with a damp paper towel on top and microwaving it in short intervals (10-15 seconds) until it softens.