If the head of a tick gets stuck in your skin, then your body will naturally form defenses against it and eventually reject it out of your body.
This is the same with any foreign object that enters your skin.
What might happen is that the body creates a "wall" around it using a bubble of fluid (like a blister for example). This isolates the tick's head.
Eventually, it will begin to grow out as the body rejects it.
If pus, swelling or soreness starts forming around the tick head though, you need to see a doctor as this will likely be signs of an infection.