This paper studies the impact of downward wage rigidity on wage and employment dynamics after the outbreak of major recessions in Spain. Downward wage rigidity stems from collective agreements, which set province-sector-skill-specific minimum wage floors for all workers. By exploiting variation in the renewal of collective agreements, we find that those signed before the onset of recessions settle on higher nominal negotiated wage growth than agreements signed afterwards. Leveraging social security data and the distribution of the worker-level bite of minimum wage floors, we document that the negotiated wage rigidity translated into higher wage growth mainly among workers with near-floor wages. Consequently, these workers experienced a substantial and highly persistent increase in the probability of non-employment, but only if they were covered by long-duration collective agreements. Our findings highlight the interplay between rigidity at different parts of the wage distribution and labor market institutions and identify conditions under which collective contract staggering and the inability to renegotiate may amplify aggregate shocks.