Perhaps it would need a new flavour of file descriptor, [...]
Linux has apparently done this: pidfd (file descriptors representing
a process). The idea is that you can pass them to various system
call variants that otherwise take pids, without the risk that the
process has exited in the mean time and the pid re-used.
I've been thinking about something like that myself, starting with
AF_PID sockets, then deciding they wouldn't/couldn't work (as think I
mentioned in this thread, the socket infrastructure really wants the
contents of a socket to be independent of who's accessing it).
Personally, I've wanted it as a way to provide an out-of-band channel
to userland programs (like a control command channel for various
daemons), but...hmm.
Feels strange to find an idea I like coming from Linux.