What is the ruling regarding a sick girl with a malignant disease abstaining from fasting Ramadan, given her inability to pay the Fidyah, in addition to her inability to eat?

If you are ill and unable to fast, then you are not obligated to fast. If the illness is hoped to be cured, then you must make up the missed fasts when you are able, and there is no expiation (kaffarah) or feeding (it'am) required of you. However, if doctors have determined that the illness is chronic and not expected to be cured, then you must pay the fidyah, which is feeding one poor person for each day.