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Weak first-story buildings are susceptible to experience severe structural damage, and even collapse, during strong earthquakes as was evidenced during the September 19, 2017 (M w = 7.1) intraslab earthquake that hit Mexico City. Such type of buildings are prone to exhibit a negative slope in their capacity curve due to weak first-story mechanism that might lead to dynamic instability during earthquake excitation. Therefore, this paper presents the main results of an investigation focused on evaluating the collapse strength ratios, R c (i.e., the normalized lateral strength ratio in the onset of dynamic instability) of single-degree-of-freedom (SDOF) systems whose force-displacement nonlinear envelope (backbone) behavior is representative of that observed in existing multistory weak first-story buildings. Particularly, their envelope exhibit several levels of negative slope after a post-yield displacement ductility capacity. Median and dispersion of R c ratios were obtained for degrading SDOF systems subjected to a set of 136 earthquake ground motions recorded in soft soil sites of Mexico City from instraslab earthquakes. Results of this investigation showed that R c ratios depend on the normalized period of vibration with respect to the predominant period of the ground motion, T/T g , the displacement ductility capacity, μ c , and the negative slope after peak strength, α c. Additionally, the spectral trend of R c ratios at soft soil sites is different to that reported for firm soil sites. A continuous functional form is introduced to obtain estimates of median R c ratios for the preliminary seismic assessment of weak first-story buildings in this seismic environment. • Dynamic instability in buildings can be evaluated through collapse strength ratios Rc. • Rc ratios follows a different spectral trend for soft soil sites than for firm sites. • Displacement ductility capacity of structures is beneficial to increase Rc. • Robust equation to estimate median Rc is proposed based on statistical results. [ABSTRACT FROM AUTHOR]