Yes, believe it or not, it is possible to reliably estimate the probability of a company going bankrupt! The z score was published in 1968 by renowned professor of the NYU Stern School of Business Edward I. Altman.
The z score has since been used to measure the financial distress of a company i.e. its financial health. The z score is linear combination of various ratios and weighted coefficients of firms that declared bankruptcy and matching them to a set that survived bankruptcy in the same industry.
The predictive accuracy of Altman’s z score is remarkable, attaining up to 90% accuracy for a one year time horizon and 72% for a two year horizon!