What should one do with those core files?

Make sure the complete CORE file was written out. System administrators usually limit core size to avoid dangerous core files filling file systems. Core file size can be limited with the "ulimit" or "limit" commands. Look at these examples:

$ ulimit -a    # Display limits for your session under sh or ksh
$ limit        # Display limits for your session under csh or tcsh

$ ulimit -c SIZE_IN_BLOCKS       # Limit core size under sh or ksh
$ limit coredumpsize SIZE_IN_KB  # Limit core size under csh or tcsh

If you see a core file lying around, just type "file core" to get some details about it. Example:

$ file core
core:ELF-64 core file - PA-RISC 2.0 from 'sqlplus' - received SIGABRT

Run the Unix process debugger to obtain more information about where and why the process abended. This information is normally requested by Oracle Support for in-depth analysis of the problem. Some example:

Solaris:

$ gdb $ORACLE_HOME/bin/sqlplus core
bt                 # backtrace of all stack frames
quit

HP-UX, Solaris, etc:

$ adb $ORACLE_HOME/bin/sqlplus core
$c
$q

Sequent:

$ debug -c core $ORACLE_HOME/bin/sqlplus
debug> stack
debug> quit

Note: Some Unix operating systems use debugger commands like sdb, xdb, dbx, etc. The same principles apply; do a man on the command and go for it!