Extra Prompt Displayed in GNU Readline

I'm writing a shell-like program in C using GNU readline and have encountered a bug related to prompt handling.

Brief Description of the Issue

In my program, after exiting a heredoc with ^D and then pressing ^C at the main prompt, an extra prompt appears unexpectedly.

$ <<a    # Start of heredoc
>        # User inputs ^D to exit heredoc
$ ^C     # User inputs ^C at the main prompt
$        # An extra prompt appears unexpectedly
$

Reproducing the Issue

The code snippet below is a simplified version and doesn't exactly replicate my entire shell program, but it demonstrates a similar issue with prompt handling.

#include <signal.h>
#include <stdio.h>
#include <stdlib.h>
#include <readline/readline.h>

volatile sig_atomic_t g_sig;

void handle_sigint(int sig) {
    g_sig = sig;
}

int readline_hook(void) {
    if (g_sig == SIGINT) {
        rl_replace_line("", 0);
        rl_on_new_line();
        rl_redisplay();
        rl_done = 1;
    }
    return 0;
}

int main(void) {
    char *line;
    signal(SIGINT, handle_sigint);
    rl_event_hook = readline_hook;
    while (1) {
        g_sig = 0;
        line = readline("$ ");
        free(line);
    }
}

Question

How can I resolve the issue where an extra prompt is displayed in readline? What do I need to do to fix it?