Archived research data can (and should) be published. Data publication is a somewhat misleading concept. What is being published is the metadata of your data package. The data itself remains stored in the archive, e.g. YoDa, DataVerse of FigShare. Once you publish your data you get a DOI and are able to refer to the storage location of your archived data package. Please note that you can also (and should) publish Closed Access data. Your data package becomes findable, but the data remains closed, as the package itself is closed access.