My mom has stage IV lung cancer and my dad has alzheimers. I can't afford to take care of them much longer. I will loose my own home. What options do I have?

It sounds to me as if you need to get them on Medicaid. They will qualify if they don't have much money. They will then likely go to a nursing home. Your mom can get hospice care anywhere - hospice works with the nursing home staff. Your dad may need a secure environment. Please check with your Social Services about this. You - and they - need help.
Take care,
Carol

Medicare typically covers hospice too. You could even select a facility or program in yoru community and meet with them to see what's possible; they will be very aware of funding options for facility based or in-home care..