Open Question: I received a 10 day notice to quit?

This is my mothers apartment, rather the lease is under her name. We have 6 weeks left for the lease to expire. My mother is back and forth taking care of her business in another state. I agreed to stay in her apartment during the time that shes away. I received a notice on the door the other day, stating that i have 10 days to quit. Only those that are not on the lease. What do I do? How can they prove that I am staying there?