In most UNIX flavored OSes, a process can be delivered a signal so that it dumps a core file. A core file is essentially a snapshot of the process and its state right before it cored (crashed or dumped). A core file is a type of ELF file that is primarily made up of program headers and memory segments. They also contain a fair amount of notes in the PT_NOTE
segment that describe file mappings, shared library paths, and other information.
A core file by itself is not especially useful for process memory forensics, but it may yield some results to the more astute analyst.