A friend of mine and his wife have been living in her grandmothers house in Kentucky for over a year with no rental agreement and never being asked to pay rent, now they fear that she may try to kick them out because she is mad at them. What rights do they have?

They have the right to be treated as a periodic (month to month) tenant. Which means they have to be given legal notice to vacate and then go thorugh the eviction process.