I want to estimate the triangular system GSEM with correlated errors in order to control for the endogenous regressors in the estimations. Thus the model contains outcome equation y=bx+az+u and selection equation z=b*x+v, where y and z are endogenous and corr(u,v)!=0. The current version of BRMS allows using set_rescor(FALSE) for binary outcome models, but is there any workaround or set_rescor serves totally another purpose which I have missed?

Please also provide the following information in addition to your question:

Currently, residual correlations can only be estimated (a) for gaussian and student-t models where we have appropriate multivariate distributions or (b) for multivariate models where all response distribution do not have an overdispersion parameter so that we can model the overdispersion via random effects which can then be correlated. Techinally the bernoulli distribution falls into category (b) but has the problem of residuals / their variance not being identiable.

In other words, given that I understand you question correctly, there is currently no way of introducing rescor for dichotomous responses in brms.