Hello Alex_Scerus,
The process you mentioned is related to a new processor that was rolled out to the service to fix public folder dumpster issues called "PublicFolderInvalidDumpsterFixingProcessor"
I assume that this process started, and fixed (almost) *all* folders, since we were migrating without dumpster? Correct? -> Yes it should have created dumpsters to each migrated public folder and you can verify that using the script mentioned here.
Does this mean that, more or less, the complete hierarchy was being changed by this process? -> The processor has just created and attached dumpster folders for each migrated public folder to handle/store deleted items inside.
Right now we are facing issues described above (e.g. folders, items can't be deleted) and it seems that the hierarchy sync has troubles to sync the mailboxes serving the hierarchy. -> for the 1st part might be that PublicFolderInvalidDumpsterFixingProcessor has failed to create dumpsters for your migrated public folders so as a result we involve our product engineering team to investigate & fix that matter since, in regards to the 2nd part what kind of troubles are you referring to?
Additional it would be nice to learn more about all processes... what, when, how, since it looks like those are not well documented, additionally it seems that MS support is also not aware of this stuff: -> Not all these processors are documented I'll the add below what is publicly existing, hope that helps.
PublicFolderHierarchySyncProcessor -> https://techcommunity.microsoft.com/t5/exchange-team-blog/introduction-to-public-folder-hierarchy-sync/ba-p/609344
PrimaryPublicFolderMailboxProcessor
PublicFolderItemProcessor
PublicFolderDiscoveryHoldsProcessor
PublicFolderItemProcessor_DueDateForUsageStatistics
PublicFolderSplitProcessor -> https://techcommunity.microsoft.com/t5/exchange-team-blog/how-exchange-online-automatically-cares-for-your-public-folder/ba-p/2050019
PublicFolderMailboxRemovalProcessor
PublicFolderMailboxMaintenanceProcessor
PublicFolderInvalidPermissionsCleanUpProcessor -> https://techcommunity.microsoft.com/t5/exchange-team-blog/announcing-the-public-folder-consistency-agent-for-exchange/ba-p/609273
PublicFolderInvalidDumpsterFixingProcessor -> mentioned here
Let me know if you have further concerns.
Regards,
Hazem