Log in to wordpress after executing another form function

If you hook wp_authenticate on a normal form submit, you can make a quick detour to your subscribe function before you continue to authenticate.

add_action( 'wp_authenticate', 'wp_authenticate_by_email' );

function wp_authenticate_by_email( $username ) {

    // check for subscribe action
    $is_subscribe="yes" == $_POST[ 'subscribe' ];

    // invalid username 
    if ( ! username_exists( $username ) ) {

        // lookup as email
        $user = get_user_by( 'email', $username );
        if ( $user ) {

            $email    = $username;
            $username = $user->user_login;

            if ( $is_subscribe ) {

                // subscribe to mailing list
                do_subscribe( $email );
            }
        }

        return;
    }

    // lookup user by login
    $user = get_user_by( 'login', $username );
    if ( $user ) {

        // get email from user login
        $email = $user->user_email;
        if ( $is_subscribe ) {

            // subscribe to mailing list
            do_subscribe( $email );
        }
    }
}

function do_subscribe( $email ) {

    if ( empty( $email ) ) {
        return;
    }

    // maybe check for password ????

    // do subscribe actions

    sleep( 2 );
}