Screen or tmux. I tend to prefer tmux, but the both have this ability. I'm actuality surprised that there isn't a more elegant choice other than redirecting stdout and stderr to /dev/null where you can fork jobs to a background and reattach later to see the tty. Is there a shell that has a job queue that can be accessed from any number of shells?

There's this for attaching a running program to your terminal when it is not started in screen: https://github.com/nelhage/reptyr