When a new process is created (see Creating a Process), it inherits
handling of signals from its parent process. However, when you load a
new process image using the exec function (see Executing a File), any signals that you've defined your own handlers for revert to
their SIG_DFL handling. (If you think about it a little, this
makes sense; the handler functions from the old program are specific to
that program, and aren't even present in the address space of the new
program image.) Of course, the new program can establish its own
handlers.
When a program is run by a shell, the shell normally sets the initial
actions for the child process to SIG_DFL or SIG_IGN, as
appropriate. It's a good idea to check to make sure that the shell has
not set up an initial action of SIG_IGN before you establish your
own signal handlers.
Here is an example of how to establish a handler for SIGHUP, but
not if SIGHUP is currently ignored: