Is this possible? I have found a few results googling this, but only of people asking the question, never answering it.
Interesting question, I cannot find any reference to unresolved in the apex language reference guide, there is nothing useful online that I can find either apart from a way to query unresolved tasks (subject name LIKE '%Unresolved'). People have stated that even cloning those records doesn't work in terms as marking unresolved. My best guess is that a hidden field manages it and salesforce restrict access for whatever reason. Maybe raise a case to support / start an idea to open up access to that functionality.
// Link to unresolved items for those that have not seen it.