I experienced this with kmail when connecting a hotmail.fr imap acount (this seems to be microsoft essentially) which contains a large number (more than 5000) of messages. The problem was that kmail/akonadi failed when downloading the messages in a catastrophic way: It would download an even much larger number of messages (apparently identical messages multiple times) until the harddisk was completely full with 10s of gigabytes of messages. It will probably be hard for someone else to reproduce it but the fix I had for it may give a hint on where the origin of the problem is: I first tried to use the command line application isync which can synchronize an imap directory with a local folder. The result was that it failed as well, after downloading a few messages it stopped. Then I tried to set 'PipelineDepth' in the configuration file to 100. Then it worked. It seems that this imap server (maybe in violation of the protocol) stops without proper fail state when too many commands are received. Kmail/Akonadi apparently do not detect this and download in repeated attempts the same messages again. Reproducible: Always
It seems that limiting the number of imap commands would fix such problem or at least the system can ask the user whether really 10 gigabytes of messages should be downloaded the prevent the system from crashing. I wanted to add that, after moving the messages with isync, the same mail account with fewer messages worked perfectly well since month.
This bug has never been confirmed for a KDE PIM version that is based on KDE Frameworks (5.x). Those versions differ significantly from the old 4.x series. Therefore, I plan to close it in around two or three months. In the meantime, it is set to WAITINGFORINFO to give reporters the oportunity to check if it is still valid. As soon as someone confirms it for a recent version (at least 5.1, ideally even more recent), I'll gladly reopen it. Please understand that we lack the manpower to triage bugs reported for versions almost two years beyond their end of life.
Just as announced in my last comment, I close this bug. If you encounter it again in a recent version (at least 5.1 aka 15.12, preferably more recent), please open a new one unless it already exists. Thank you for all your input.