Dumping process memory
Every Linux process has a pseudo mem device which can be used to read the process's memory pages. This mem file is found under /proc/$pid/mem. In order to properly use this file, you have to read the readable sections as outlined by its corresponding maps file.
Simply dd if=/proc/$pid/mem would not work as you will end up reading invalid or non-readable pages, resulting in a Input/output error. Instead, you should opt to use gdb to create a a core dump (using gcore $pid). On systems without gdb (think embedded systems), you may try to do this with the following bash-only solution.
Dumping process memory using Bash
# PID=$pid cat /proc/$PID/maps \
| grep -ohE '[a-f0-9]+-[a-f0-9]+ r' \
| tr - ' ' \
| while read s e foo ; do
echo "Dumping $s to $e"
dd if=/proc/$PID/mem bs=1 skip=$((0x$s)) count=$((0x$e - 0x$s)) >> /tmp/dump
done