Typically from an insurance company. If you were injured in a car accident, the company which provided insurance coverage for the other driver, or his employer, will be involved. If the other driver was uninsured, negotiations may be with your own insurer.
Doctors, hospitals and other healthcare professionals who may be named in a medical malpractice action will have insurance carriers who vigorously defend their clients. In the case of a severe injury or multi-vehicle accident, there may be several insurance companies involved – another reason why it is best to leave settlement negotiations up to your legal advocate.