The cold hard fact is .. You are bound by laws that protect tentants. Whether or not he/she is ill is irrelevant. As long as the rent is being paid, and the tenant is still staying within the boundaries of your rental agreement, there is no reason to 'do' anything.
If however, the rent is not being paid .. Then you 'can' take legal action to evict the tenant.
However .. It all still also weighs on your moral obligations .. THAT is a personal choice on how to handle a case of someone who has 'no one'. That is a matter of your own conscience. You CAN take the steps to help this person gain the help they need and treat that in a way that will help you sleep at night.