Long-running processes are definitely possible. You obviously have to be a bit more careful not to leak memory.

It's common to have things like queue workers implemented as long-running CLI processes. I just checked one of our services at work and there's a queue process that has been running for more than 4 months. There might be others that have been running even longer, but I don't feel like checking every service right now ;)

Projects like Swoole or ReactPHP are trying to make similar things possible for serving web requests too.