Asbestos lodged in the skin can be gently pulled out, if there is any residue, you need to go to the hospital to have it removed by a medical professional and have the wound treated.
Asbestos is thin and tough, so if it is touched without proper protection, you may be stung and feel a localized foreign body sensation. If the asbestos is lodged in the skin more obviously, it can be taped out or picked out with a sterile needle and the skin sterilized with iodophor solution.
If there is any residue that has been in the skin for a long time, it may lead to infection, so you need to go to the hospital to find a professional doctor to pull it out, and then disinfect the local skin after removing it to prevent it from becoming infected. If infection has occurred, you can use topical mupirocin ointment and so on.