When downloading article citations from databases the Library subscribes to, Zotero will download a PDF of the article if it is available (as long as you have your preferences set for it to do so). Zotero has recently announced an enhancement that makes it easier to locate PDFs when they aren’t available in the database. It can now search Unpaywall, a database of open access articles. It will also perform this search if you add an item to your library using its identifier. For existing items in your library, you can choose the “Find Available PDF” option in the item context menu. (Note that “Find Available PDF” will only be shown if the item has a URL or DOI, because URL-based lookups require one of those two things and Unpaywall requires a DOI).
To use the new feature, update to Zotero 5.0.56 and update the Zotero Connector to 5.0.41.