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We investigate whether heightened disaster risk increases government debt, undermines fiscal sustainability, and disproportionately affects low-income households. Using panel local projections from 1995 to 2021 across 184 economies, we find that climate vulnerability shocks worsen debt dynamics, reflected in higher debt-to-GDP ratios and deteriorating fiscal balances. These shocks also heighten income inequality, with the income share of low-income groups declining relative to that of high-income groups. A state-dependent analysis reveals that these effects are most severe in high states of climate risks. Motivated by this empirical analysis, we develop a new Keynesian dynamic stochastic general equilibrium model featuring two household types and a fiscal authority employing targeted policies. Disaster shocks induce recessions and intensify consumption inequality. Consumption among hand-to-mouth households declines by a factor of three compared to Ricardian households. Sovereign debt increases sharply as governments implement measures to cushion the economic blow. However, targeted transfers effectively reduce inequality at a lower fiscal cost than progressive income taxes. Our findings suggest that designing climate-resilient budgets and equitable relief measures is essential to preserving both fiscal solvency and social cohesion in the face of growing disaster risk.