Processes backgrounded via `bg` or `&` will typically die under 2 scenarios:
1. The shell receives a SIGHUP
2. They try to write to a terminal which no longer exists.
Item #1 is the primary culprit when closing your terminal. However whether it happens or not depends on **how** you close your terminal. You can close it by:
1. Something like clicking the "X" in your window manager
2. You can type `exit`, `logout`, or `CTRL`+`D`.
Item #1 is the one that will result in a SIGHUP being sent. #2 does not.
So long story short, if you background a process with `bg`, and then log out with `exit`, `logout`, or `CTRL`+`D`, the process will not be killed.