If I SSH into a remote machine and my connection gets dropped, then is there a chance that the run I made will continue on?

Question

Or will the run halt along with everything (though maybe partial progress could be made if I use a ">" to print progress so far to a file)

Answer 1

The process (your "run") will receive a SIGHUP and will likely terminate. Not all programs terminate properly, for example, vi/m. You can run the program with nohup to have the program ignore the SIGHUP signal. For a running program, you can send it to the background with Ctrl+Z then type disown.

You should look into screen(1) or tmux(1). These create sessions with multiple terminal windows and allow you to reattach after being disconnected.