D.C. offers an Emergency Tenant Assistance Program that helps low-income tenants. Other federal programs (e.g., FEMA) may also provide additional assistance to tenants and landlords.
Under the Emergency Tenant Assistance Program, low-income tenants can apply to be considered for financial assistance for housing, including “to assist households faced with sudden, unavoidable displacement from a dwelling unit for reasons such as a fire or other disaster that occurred through no fault of the applicant.” Your income must be below 125% of the monthly federal poverty level according to household size. Tenants can find more information here: https://dhs.dc.gov/service/emergency-rental-assistance-program. D.C. Municipal Regulations 14-1703.
If a place is “unsafe or unsanitary” due to fire damage, tenants are free to move out and break leases under the implied warranty of habitability. Tenants should notify their landlord. D.C. Municipal Regulations 14-302.
Tenants and landlords may find federal programs and assistance from non-profits that have programs to help in the case of fires.