I am not licensed to practice law in Indiana so the following should not be taken as legal advice, but simply as information based on general principles of law which is intended to educate. If you need legal advice, please consult a lawyer who holds Indiana licensure.
When you die, your creditors may file claims against your estate, and the executor of your will is responsible to pay the claims made by the cutoff date. If there is not enough money to pay the claims, the estate is insolvent. The unsecured creditors are out of luck (i.e. the credit card lenders).
Consult with an estate planning lawyer in Indiana. There are ways to convey your interest in your house to your son (for example, a revocable trust that becomes irrevocable upon your death, with your son as substitute trustee) that will bypass probate and protect the equity in your home from the claims of any unsecured creditors you may have at the time of your death.
Debts follow the property or person who created the debt. If your son did not sign anything agreeing to be responsible for the debt then he will have no personal liability.
However, in the case of a mortgage the real estate is security for the outstanding balance. If the mortgage is not paid off by your estate or your son through his own financing then your lender can foreclose on the property and collect its balance that way. In this case your son is not responsible for the mortgage, but your house is.