Why does calling kill(getpid(), SIGUSR1) inside handler for SIGUSR1 loop?

Question

I'm trying to understand what is happening behind the scenes with this code. This was asked at a final exam of an Intro to OS course I'm taking. As I understand it, when returning from kernel mode to user mode, the system checks if there are any pending signals (by examining the signal vector) and tends to them. So as the program returns from the kill syscall the OS sees that SIGUSR1 is pending and invokes the handler. By that logic, the handler should print "stack" in an infinite loop, but when running this code it actually prints "stackoverflow" in an infinite loop. Why is this happening? Thanks in advance.

void handler(int signo) {
    printf("stack");
    kill(getpid(), SIGUSR1);
    printf("overflow\n");
}

int main() {
    struct sigaction act;
    act.sa_handler = &handler;
    sigaction(SIGUSR1, &act, NULL);
    kill(getpid(), SIGUSR1);
    return 0;
}