A collapsed heating plate in an old rice cooker may cause some problems, but it will not directly lead to a fire. A collapsed heating plate in a rice cooker is usually caused by long-term use and wear and tear. When the heating plate collapses, it may result in uneven heating or inability to heat the food properly, thus affecting the cooking results.

However, it's important to note that if there are other faults inside the rice cooker, such as short circuits or deteriorated power supply lines, these problems may increase the risk of fire. Therefore, if you notice that the rice cooker heating plate is collapsing and there are other abnormalities, it is best to stop using it and send it for repair or replace it with a new one.

Overall, while a collapsed heating plate by itself won't directly cause a fire, if the rice cooker is otherwise malfunctioning or damaged, you need to use it with caution to ensure safety. If you have any concerns about the safety of your rice cooker, it is recommended that you consult a professional or review the relevant product manual.