// server
bool is_server_disconnected(int client_socket)
{
    // 
    set_flag(client_socket, O_NONBLOCK);
    char buffer[10];
    int length = recv(client_socket, buffer, 10, 0);
    clr_flag(client_socket, O_NONBLOCK);
    return length == 0;
}

set client_socket to non-blocking, and then if recv returns 0, it means remote socket is closed.

When a stream socket peer has performed an orderly shutdown, the
return value will be 0 (the traditional "end-of-file" return).

Linux man

tcp disconnect is not considered for the time being. I wonder if there is a simpler and better way?