If I get evicted for non-payment of rent, how long will I still be able to live at the rental residence? What are "squatters" rights?

I have been renting a condo from a private party. I have lives here for 3 years. I lost my job some months ago and as of yet, have not been re-employed. I am afraid that within the next couple of months my landlord may evict my daughter & myself. I am wondering how long the eviction process typically takes? Might I be able to still live in the residence while the process is going through the courts? My mom mentioned that I may have "squatters" rights: do I? Plz. help. I have always paid rent in cash to my landlord & recently stopped getting receipts from her. I am on a month to month lease now.