The Core.* file (usually called core.1234, core.1987, core.1673 etc.) is a dump file that is generated when a customer's (PHP) script crashes during execution. This file contains information from the process results stored in server memory when it crashes.
The size of the Core.* file depends on the amount of memory used when executing the script and crashing, the larger or more Core.* files mean that scripts that crash are often executed.
The solution to avoid this Core.* file is to fix the script that crashed and also not use Plugins / Modules / CMS that require high resources.
These Core files can be analyzed with the :
strings /home/user/public_html/core.xxxx |head
or with
gdb /usr/bin/php /home/user/public_html/core.xxxx
From the results of the analysis, information will appear on which script crashed.