If your property has not been fully vacated and has furniture, personal belongings or garbage in it, call your landlord immediately, give a verbal report of your findings and ask that the mess be dealt with immediately. Follow up all phone calls or in-person conversations with written documentation stating your understanding of what will be done by when. Keep a copy of all correspondence.
Remember, every tenant has the right to a premise that is fit for immediate occupancy!
The Landlord will insure the building with respect to liability and property damage but, while the Landlord and Tenant's liability coverage may overlap, the property insurance covered by the Landlord does not cover the interior contents of the Tenant's space.