This issue is caused by missing outbound mappings between Provisioning Server and IM and can be resolved by restoring the required mappings.
In the Identity Manager Management Console go to Environments > [your environment] > Advanced Settings > Provisioning
The outbound mappings should contain at least the following:
If any of these mappings are missing they can be added by selecting the user event and outbound event from the drop down menus and hitting the add button.
Once this is done click the save button and restart the environment. After the environment is restarted Inbound Sync should resume normal behavior.