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Renters Liability in Case of Liability Claims for Property Damage or Fire
According to US News, renter's insurance does cover liability as well as your own belongings.  They list this as one of four "myths" often promulgated about renter's insurance.  This is backed up by esurance.com, which explicitly mentions "Property damage to others" as covered.  Nationwide Insurance says that renter's insurance covers "Personal liability insurance for renters" and "Personal umbrella liability insurance".  Those were the first three working links for "what does renters insurance cover" on Google.   In short, while it is possible that you currently have a different kind of coverage, this is not a limitation of renter's insurance per se.  It could be a limitation in your current coverage.  You may be able to simply change your coverage with your current provider.  Or switch providers.  Or you may already be covered.   Note that renter's insurance does not cover the building against general damage, e.g. tornado or a fire spreading from an adjacent building.  It is specific to covering things that you caused.  This may be the cause of the confusion, as some sources say that it doesn't cover anything in the building.  That's generally not true.  It usually covers all your liability except for specific exceptions (e.g. waterbed insurance is often extra).