In reply to Loralee.

I'm going to try to sound like I know what I'm talking about.

I actually contacted Siteground about this. It appears all servers do this, no matter what CMS you are using. I read Drupal forums talking about memory dumps. You, or rather a senior server admin can limit their size, or disable them completely. You would only enable them if their was a problem, much like enabling wp debug in your config.php file. However, these core dump files are huge and practically unreadable by a human, so I'm not sure what you are supposed to do with them. But seeing as my site is loading faster than ever and all features/plugins are working, I managed to convince SG to turn this off. Why it was on in the first place was not made very clear, which is why I did my own research, aka Goooogling. With this all said, I'm not entirely sure there is a bug in WP which is causing this.