Social workers at both public and private hospitals have lists of these organisations and are meant to guide people who need to raise funds.
There are a number of organisations and its a matter of going around to all of them to raise bits of money from each. Its a pretty painful exercise.
The public hospitals are likely to have a reasonably comprehensive list. I don't know about the private/ trust hospitals.
Various community trusts also have grants for medical expenses.
Finally, hospitals calling themselves trusts are legally bound to provide a percentage of patients with free care and some with subsidised care. A government study found that only Bombay hospital actually provided even subsidised care. Even here, all drugs must be paid for.
If the person finds that trust hospitals do not offer free care, it might be worth contacting a lawyer to force the hospital to cough up. Mihir Desai in Bombay has been involved in legal action on medical negligence.