Grounds for lawsuit? Tenant Injured on Staircase

[Garrett F Anderson]

Hello BP!

I heard a story the other day from a landlord in my hometown and I wanted to ask some questions related to it concerning protection from lawsuits or who is liable.  

The situation:  The tenants live in an up/ down duplex with the only access to the upper portion of the duplex being a staircase to the second floor of the whole building.  During a recent severe storm the staircase was weakened and fell apart.  A tenant who happened to be on the staircase during the collapse was injured and missed work for 3 days.  The tenants also didn't have access to or from their home for a day while the stairs were being prepared.

My questions:

1. Is the landlord liable for the injures to the tenant, i.e. will he have a possibility of getting sued for medical bills and the missed work time?
2. Is this kind of incident covered in typical lease agreements?

The landlord told the tenants not to worry about next month's rent in order to avoid any charges against him.  How would you handle the situation and do you think he did the right thing?

Thank you for your feedback and for reading my post!