After we inherit a house, are we still responsible for the debts attached to it?

My Father is 82 years old and was diagnosed with Alzheimer's/Dementia several years ago. Since then, my mother passed away so we then took care of my father for a year in HIS home. My wife and I moved in with him after selling our home which was smaller and not equipped to take care of him properly. He took out a $50K line of credit against his home and had several credit card debts. The creditors are calling regarding these debts and I know they can place a lien on the home for them. We started paying down the line of credit just to keep the home from being foreclosed on. The home is paid for (except for the LOC) and is willed to us when he passes. It is in a Living Trust account and I am the trustee. I also have power of attorney for my father which has helped me do several things on his behalf. What steps can be taken by us to stop the creditors from placing liens on his home? Also, is there anything that can be done regarding the line of credit or these other bills because of his Alzheimer's Disease? Is there a government program to help lower or eliminate them? I know we are not responsible for his debts right now. However,when they become attached to the home (willed to us), we will in fact, be responsible, right?