These functions were originally available to programmers, and have been internalized to allow for the greater flexibility of the add_hook and run_hook functions. However, if you have existing code that you don't want to change, you can define your own versions of taskdied and taskstarted that shadow the built-in functions and do what they always used to do. Your old code will not break, but it will hide the hook version of the taskdied and taskstarted functions.

On the other hand, you could get both with something like this:

builtin_taskdied = taskdied;
builtin_taskstarted = taskstarted;

function main ()
{
    init_ipc ("x","x");

    add_hook (#taskdied_hook, #hook_taskdied);
    add_hook (#taskstarted_hook, #hook_taskstarted);

    while(t)
        next_event();
}

function taskdied (!a?...=nil)
{
    princ ("task died: ", a, "\n");
    funcall (builtin_taskdied, a);
}

function taskstarted (!a?...=nil)
{
    princ ("task started: ", a, "\n");
    funcall (builtin_taskstarted, a);
}

function hook_taskdied (!a?...=nil)
{
    princ ("hook task died: ", a, "\n");
}

function hook_taskstarted (!a?...=nil)
{
    princ ("hook task started: ", a, "\n");
}