I’m not really familiar with details, but I’m pretty certain Elixir (or rather BEAM) doesn’t need to send EOF at all. I assume that BEAM OS process owns its end of the pipes, so regardless of how BEAM OS process terminates, all its resources are closed, and the external program gets EOF when it attempts a read from its stdin. For this to happen instantaneously, the external program needs to constantly read from the pipe. If the program is busy with some other processing, it might take a long time to notice EOF. I’ve seen this situation in practice.
Ports are meant to be used with external programs which are written for to be used by them. If the program you’re using is not written for Erlang ports, you need some kind of an adapter which can handle all requirements of Erlang ports. That also means that your wrapper needs to detect the crash of the wrapped external program, and react to it by stopping itself, which should then be detectable on Elixir side of things. I never did this myself, so not sure how it can be done, but I’d be surprised if this wasn’t possible.