My apartment building caught fire 3 units down from my apartment unit. My unit had mostly water damage. I did not have renters insurance,though. The fire chief deemed the property structurally unsound and I lost everything because I could not get it out. They are starting to demo the building when I looked and saw most of my personal stuff on the back of the supervisor's truck. Does anyone know if I have a good case to sue the apartment complex insurance.

Its worth a try, especially if you have proof that your belongings were removed. A lot depends on the cause of the fire. If it was due to problems with the building, faulty wiring, etc. you would have a case against the building. If it was due to the tenant's negligence, I would also sue that tenant.

And next time get renter's insurance.

You say you saw your property in the back of the supervisor's truck? What supervisor? The apartment complex? Call the police and report your property stolen.