We had similar kind of challenge in CRM systems as well. Where the status of many CRM objects like service orders, sales orders etc was not complete , hence not archivable
These type of issues are common roadblocks in data archiving projects.
Business is also not interested in taking ownership and closing these .
If there is decommission planned for this system then ILM Snapshot function might be considered .
Snapshot
Snapshots are archiving runs that are used to extract data, but not delete it, from the database. The system does not perform any checks aside from following the restrictions in the selection variant. Accordingly, these options let you write data to the archive from active business transactions that are not yet complete. To prevent data loss, snapshot runs cannot be used for deleting. A snapshot always creates redundant copies of data in the database. This function is especially useful for system shutdowns in connection with the Retention Warehouse scenario.
Bottomline is that Prevention of data loss has more importance over archiving.