Unfortunately, this is a result of the conversion from the previous software to XenForo. The XenForo format treats private messages as private threads between members (called Conversations). The data in the Conversation table has all of the metadata to link all active participants in the private discussion.
In other forum software, there is usually no information in the message tables to link incoming and outgoing messages between members because the inbox and outbox are separate tables. The XenForo conversion doesn't know how to process the individual records, so any records that aren't associated directly to the member are discarded during the conversion.
As far as I know, there is no recovery for this. I don't have any conversations prior to the conversion, so I can't experiment with post-conversion options to try to restore the content.
What a travesty this is, years of information, contacts, numbers and address lost without a hint of it happening.
Did somebody not think some of us might have wanted to have an opportunity to save this data ?
I can't answer your question as I wasn't involved in the process here. However, I checked on the site I used to own and had converted from vBulletin to XenForo. After four months of planning, testing, and preparing the membership for the move, all of the PMs were broken as well. I have over 2,000 private messages on that site that predate the conversion and they are exactly as you described. Since I don't visit the site much and the messages are now meaningless, I will go through the process to remove them.
Andy, the problem is that the internet is inevitably a risk if you don't copy the data to some place where you control storage. Things I want to keep I screenshot and stick in a file with storage divisions. Takes no time as the screenshot saves to desktop automatically and can be dragged as an image.