What is the responsibility of a publication board in relation to ethical subject studies?
In the US, the PHS regulations are fairly specific with respect to Research Integrity and the Responsibilities of institutions, and are found in 42 CFR Part 93.

This regulations mandates that Institutions have a published policy.  Most of the requirements for that policy involve procedures for holding data, investigations, whistleblowers, and doing what they can to protect the reputations of charged individuals who are not found to have committed misconduct.  There are also reporting requiments to ORI and funding institutions.

There are no specific requirements for requesting retractions from journals.  I looked at my own institution's policy, and it does not mention retraction requests.

That said, institutions tend to do whatever they are legally required to, and whatever they can do to protect their reputations.  They are also reticent to do things that they are not required to do that might result in lawsuits.  Put all that together, with appropriate weighting, and I suppose in some cases institutions would request retractions, and in others, they would not.