I just look at the socket and notice that one of the tooth that were extracted seems like half of it is still there? how did they cleeaned the infection at the baseof the bone with that thing still there. only half teeth is missing?

Difficult to answer your question without seeing what treatment was rendered. You'll need to consult with the extracting dentist or oral surgeon.

Tnis is an educational site, not a second opinion site. We cannot examine/x-ray the surgical site. Whatnyou are looking out may be a clot, not a tooth root. Return not your treating Dentist or Oral Surgeon for post-surgical care, or seek a second opinion.