When you collect the last month's rent, and clearly label it as such, the tenant is paid up for that last month -- whenever it is, even if the rent has gone up in the meantime. You might have increased the "last month's rent" that you were holding by $50 at the time you raised the rent, but now it's too late.

For this reason, it's rarely in a landlord's interest to label deposits as the last month's rent. Far better to collect a deposit that is at or below your state's limit, and label it simply as a deposit (which you can use to remedy damage, perform necessary cleaning, and cover unpaid rent). This approach will give you flexibility when it comes to using that money, too. For example, you may need the whole amount to cover damage and cleaning, but need none of it for unpaid rent. There's no reason to sideline a large portion for the last month's rent when you can simply expect the tenant to pay for that month when it is due.