If the tenant is late on payments I would not be so lax on the payments. If the tenant is a good tenant then they need to discuss your situation with the landlord. The landlord is not your friend but they got bills to pay too. I think its better to file a notice and see if the tenant would pay the late rent.
Rent arrears is a serious thing for me, I have heard of Tenants owing a lot of money, destroying property and leaving the place in waste. As soon as rent is due and unpaid, I issue a notice to the Tenant,that this is so, and state to them when the rent should have been paid, I give Tenant one week in order to make amends, if they do not, they are issued a notice to quit and I retake possession, a home can be one of your most valuable possession, and to have that destroyed or misused by a person can be very hurtful, I implore all those who are Tenants, play fair!
I thankfully have never had to deal with this. I've learned a lot from reading this thread though. If the situation arose, how I handled it would probably depend on the tenant's history with me.