1) There is no right to stay after a lease expires--period. It doesn't matter whether you "had to."2) If someone is staying without a lease, including as a holdover tenant, they don't need to first get a notice to quit; that because they have no right to be there to begin with. Without a lease, they have no right to possession and may be evicted.3) Most commonly, holdovers are charged at their previous rent. However, since there is no lease, the landlord is not obligated to do so. I believe, though, that without notice that the rent would go up, the landlord cannot charge you at higher rate (while if you had received notice that the rent on the apartment for whomever rented it next would be X and you still stayed, then you could be charged more even as a holdever, especially if that rent could be substantiated as market rate).4) If you and the landlord can't settle, he can certainly ask for more in court; the court will determine what is the fair amount you owe. He can also send the matter to a collections agency and if you disagree, you can challenge the matter or the debt, again in court.5) It is not clear why you asked the question in the context of a retalitory eviction; it is not a retalitory eviction to evict someone without a lease who has no legal right to stay there.