How to safely close a THREAD which has a infinite loop in it

You should - literally - never use TerminateThread(). And I'm not even joking. If you are terminating a thread from the outside, all resources reserved in it will be leaked, all state variables accessed inside will have an undetermined state and so on.

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The solution for your problem might be signaling your thread to finish itself. It can be done by a volatile variable changed by thread-safe means (see InterlockedIncrement() on that), a Windows event, or something like that. If your thread has a message loop you can even do it by sending a message to ask it to stop.

The proper way is to create an event "kill me", by using CreateEvent, then flag this event when you wish to kill the thread. Instead of having your thread wait while(1), have it wait while(WaitForSingleObject(hevent_killme, 0)). And then you can simply let the thread callback finish and return, no need to call _endthreadex or such.

Example of callback function:

static DWORD WINAPI thread_callback (LPVOID param)
{
  ...
  while(WaitForSingleObject(hevent_killme, 0) != WAIT_OBJECT_0)
  {
    // do stuff
  }

  return 0;
}

Caller:

HANDLE hevent_killme = CreateEvent(...);
...

void killthread (void)
{
  SetEvent(hevent_killme);
  WaitForSingleObject(hthread_the_thread, INFINITE);
  CloseHandle(hevent_killme);
  CloseHandle(hthread_the_thread);
} 

Never use TerminateThread.

Instead of while(1), you can use while(continue_running), where continue_running is True when the thread loop should run. When you want to stop the thread, make the controlling thread set continue_running to False. Of course make sure that you properly guard continue_running with mutexes as it is a variable whose value can be modified from two threads.