The backing governs part of the item's care, so the top fabric alone is insufficient. Many layered products have restrictions that differ from plain cotton laundry.
Understanding this situation
Use the complete product label and the dryer's permitted-item guidance. Deteriorated rubber-like material can create debris or heat-related concerns, and a bag does not change that construction.
A useful next step
Keep unsuitable or damaged mats out of the dryer. Follow the specified alternative method. If backing has broken down during a cycle, stop use and arrange appropriate cleaning or assessment before processing more clothes.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.