Notes (assuming Linux): (1) It's the terminal driver that intercepts
^C or ^Z character and sends SIGINT or SIGTSTP. The terminal may be configured not to do this, so it's not necessarily that the process ignores anything, respective signal sent with kill may still work. (2) The signal (from keyboard or from kill) may work but if the parent does not properly react to SIGCHLD then you may think the child is still there silently doing something. (3) You wrote "the foreground process" (singular). SIGINT or SIGTSTP from keyboard goes to the foreground process group.