>They would write the file descriptors of connected sockets to a file, restart the process, then read the list of file descriptors back into memory and resume normal use of the socket

Nope. When a Process exits for whatever reason, the OS closes and releases all resources connected with all File/Socket descriptors for that Process.

You will have to architect your System to explicitly accommodate this scenario. Some techniques here : https://stackoverflow.com/questions/55006657/can-i-allow-my-...