It's one of those thing that sound nice on paper but a actually couple your runtime with ci/cd, if you have anything else beside Erlang what do you do? You now need a second solution to deploy code.
With rolling deployments, your only choice is to wait until that connection drains by completing or failing the download. If that doesn't fit your use case, you're out of options.
If your application is an Erlang app, you could hot code reload an unaffected part of the application while the download finishes. Or, if the part of the application handling the download is an OTP pattern that supports hot code reloading (like a gen_server) you could even make changes to that module and release e.g. speed improvements mid download stream. This is why Erlang shines in applications like telephony, which it was originally designed for.
one of the cool things about unix is (and perhaps windows can do this in the right modes, idk), the running copy of a program is a link to the code on the disk (a link is a reference to the file, without the file name). You can delete a running program from the disk and replace it with a new program, but the running copy will continue and not be aware that you've done that. You don't need to wait till the program finishes anything.
on an every day basis, this is what happens when you run software updates while you are still using your machine, even if your currently active programs get updated. you'll sometimes notice this in a program like Firefox, it will lose its ability to open new tabs; that's because they go out of their way to do that, they wouldn't have to if they wanted to avoid it, just fork existing processes.
An even cooler thing is the running code is just mmaped into memory. One of the nifty things about mmaped files is if you change the backing file, you change it everywhere.
Not my recommended way to hot load code, but it might work in a pinch.
unlink, replace, start a new one, have the old one stop listening does work for many things. Some OSes have/had issues with dropping a couple pending connections sometimes; or you have to learn the secret handshake to do it right. A bigger problem is if your daemon is sized to fit your memory, you might not be able to run a draining and a filling daemon at once.
It also doesn't really solve the issue of changing code for existing connections, it's a point in time migration. Easier to reason about, for sure, but not always as effective.