This is a good question, and there were at least a couple routes we could have taken for this. The situation described is when you have a two-stage choice, where the choice in the second stage is dependent on the first stage choice. To set the stage, imagine there are two items on the menu, making up dependent variables, DV1 and DV2. Imagine that DV2 is only available to be selected if DV1 was selected.
We do this by estimating a model for DV2 for only the tasks where DV1 was chosen. But, this can mean that no information is available for building a DV2 model for a respondent (under HB) if that respondent never picked DV1.
We decided to make individual-level MBC simulations (resulting from HB) use a set of utilities for each respondent, even if that respondent didn't see any tasks for the model due to a conditional dependent variable relationship (2-stage choice) like the above. Let me explain why it works out.
We multiply the predicted probabilities for the DV1 model by the predicted probabilities for the DV2 model to obtain the likelihood of the respondent selecting DV2. For a respondent who never selects DV1, the predicted likelihood that he would select DV1 is of course extremely close to zero. For DV2 predictions for such a respondent (who never had an opportunity to select DV2, since he never selected DV1), we use the population means for the DV2 model parameters to predict the likelihood that he'll select DV2 GIVEN that he has selected DV1. However, for this respondent, the likelihood of selecting DV1 is extremely close to zero, so it matters very little what predictions we make for this respondent for the DV2 model. Making predictions for DV2 based on the population means therefore seems a reasonable thing to do for such a respondent.
This approach kept all respondents having complete information for all dependent variable models, which made the software development task a bit easier. It also reflects the fact that there is a non-zero likelihood that such a respondent would be predicted to pick DV2 given a new opportunity, which makes sense.