I had a similar experience many years ago, but the e-mails weren’t a decade old, only months.
What happened was that the e-mail system would occasionally spool a message and forget about it, but it didn’t do it all the time. Since it only lost track of messages once in a while, no one really noticed. After all, how do you notice not receiving a message that you didn’t know was coming? Once in a while someone would lose a message that they knew was coming, but since the e-mail system otherwise worked fine and didn’t lose most messages, it was just shrugged off as the message getting lost somewhere on the internet and no one gave it a second thought.
Until the machine finally spooled up so many lost messages that it completely filled its disk. Which was followed by the machine promptly crashing.
The folks in charge of the machine finally figured out what was happening, and all of the messages that the machine had spooled up and lost over the preceding months (maybe even a couple of years, I don’t remember) were all sent out at once. along with a message explaining what had happened.