Some JIRA servers can be configured to prevent any issue from being unassigned at all. Unito however syncs with other apps which generally do allow unassigned tasks and issues. To avoid errors and confusion, we prevent the creation of syncs with such JIRA projects, and you'll get the error:
The JIRA instance does not allow unassigned issues.
You'll need to change that project's configuration in JIRA before it can be synchronized. The details can be found in JIRA's documentation under Allow unassigned issues.