A renter have a fire (a) in that home and the landlord's insurance pays for the overexploit does renter reward ins. posterior?

Answers: That does not make sense at all

The with the sole purpose way would be if the renter was guilty of setting/causing the fire intentionally.
The landlord's insurance company have the right to go after the tenant, if the tenant caused the fire (accidentally, premeditated, or through negligence).

So, yes.
In many cases, the landlord's insurance will seek compensation from the tenant who cause the fire, after the insurer has paid the tenant to repair the damages. It makes no difference if the tenant caused the fire intentionally or accidentally. One of the BEST reason to carry renter's insurance, since such insurance will step in to cover any liability to the tenant.

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