Residual dependence and responses patterns

Hello, I am not an expert in IRT, but I am trying to understand better how residual dependency happens. Suppose I have a 2PL probit model with some prior distributions for the abilities theta and items parameters (difficulty and discrimination), so I was wondering what pattern should we observe in (binary) matrix of answers Y (p x n) (p: number os persons and n: number of items). I know there are some methods for detecting residual dependency, but apart from this mathematical view, what kind of pattern of answers I would expect between two items that are correlated? For example, given that theta and the item parameters have flat priors, in an extreme case, two identical patterns of answers across all the persons, would reflect a residual correlation that will be captured through some association estimated parameter or correlation matrix.