Yes ma’am, the parents of your cousin can sue the hospital for medical negligence. Please bear in mind that it’s your responsibility to prove negligence, on the part of the hospital, if you decide to sue them. Basically, the burden of proof is on you.
You should first file a complaint to the State Medical Council against the concerned medical practitioner. They will conduct the investigation.If the hospital is found to be at fault, then the council will make a report and take action.
If you are seeking monetary compensation, then it would be prudent to approach a consumer court. There are various forums. As per the amount of compensation you may approach one. Also you should act promptly because section 69(1) of Consumer Protection Act, 2019 says that a complaint must be made within 2 years of the date of the injury.
My personal suggestion to you would be to hire a Patient-Advocate. They are experts in this field and have relevant knowledge along with similar case experience. He will be capable of proving Medical negligence if any.
Though Section 80 of IPC can be used as a defence by the hospital authority that ‘nothing is an offence which is done by an accident, in the doing of a lawful act’. But they still have committed a nonfeasance. Which gives you a right to be compensated under the Law of tort.