# Binary outcomes with low goodness of fit (GOF) but good predictive power?

We know that it is possible that a model predicts the outcome reasonably well (and hence high R-square) but is actually misspecified (and hence low goodness of fit), as this example shows.

The outcome of that example is a continuous variable. I am sure there are thousands of similar examples for binary outcomes, but it is just hard for me to imagine one. Can anyone find such an example for me that shows a model predicts the binary outcomes well but is actually misspecified, causing low goodness of fit? I'd appreciate it.