I have successfully handled cases like this. Nursing homes are required to assess you father's risk of falling and prepare an appropriate comprehensive care plan. Illinois and Federal law require nursing home to "provide the necessary care and services to maintain the highest practicable physical, mental, and psychosocial well-being, in accordance with the comprehensive assessment and plan of care."
You need to retain an attorney to investigate whether the nursing home fulfilled its obligations. In my experience, nursing homes are often understaffed and pursue profits over safety.
Please let me know if you have any additional questions. I wish your father a speedy recovery.