Dedupe Folder shows offline in Storage Tab of Backup Exec UI.
Adamm.log in BE Install folder\Logs shows as below :

Dedupe\Log\Spoold\BEServerName\pvlsvr.exe\Store shows as below -

The Deduplication volume was full. Some data was copied into the Dedupe volume, which left no space for backups on this storage. The setting in Deduplication Storage properties "Percentage of disk space to reserve for non-Backup Exec operations" was set to 0.
1) The setting in Deduplication Storage properties "Percentage of disk space to reserve for non-Backup Exec operations" should not be changed. By default, it is set to 5.
2) Ensure crcontrol.exe --dsstat command when run from BE install path using the command prompt returns at least 85 percent usage. Backups to deduplication can run till 95 percent usage.
It should be understood that the storage size and retention settings should be chosen in such a way that there should be an equilibrium maintained between what's being stored in Deduplication Storage and what is expiring and being removed. At 95 percent usage and the "Percentage of disk space to reserve for non-Backup Exec operations" if set to 5 , the dedupe folder should remain online and at that stage move out any folder/files not related to deduplication storage folder (from outside the BackupExecDeduplicationStoragefolder) to make space for dedupe to run its house keeping activities. (The volume should be dedicated to dedupe and any other folder taking up space on the dedupe volume apart from the dedupe storage should be moved to a different volume). Ensure to reclaim space and lower the space utilization of dedupe so that backups can be accommodated. Follow article 100008765 to understand how to reclaim space from the deduplication storage folder.
3) Once enough space is available, restart BE services and dedupe folder should come online. Ensure Dedupe services are running as well. If sufficient space is available and the errors are different then same solution may not apply and technical support will need to be involved then.