Firefighters let house burn down

No insurance means no coverage.

In your world, if you get sick, sue a doctor! They should have helped you though they have no obligation to do so. Matter of fact, sue every doctor you can find.

That's actually how it works mind you :/

Failure to provide medical treatment

In general terms, doctors and hospitals have a duty to provide appropriate care for their patients, and an omission may breach that duty except where an adult patient of ordinary capacity terminates the duty by refusing consent. There is a conflict in public policy. The policy of patient autonomy enshrines a right of self-determination—patients have a right to live their lives how they wish, even if it will damage their health or lead to premature death. Society’s interest is in upholding the concept that all human life is sacred and should be preserved if at all possible. It is now well established that the right of the individual is paramount. In Re C (Adult: Refusal of Treatment) (1994) 1 WLR 290, a patient diagnosed as a chronic, paranoid schizophrenic refused to allow his gangrenous foot to be amputated. This was permitted because his general capacity showed him capable of understanding the nature, purpose and effect of the life-saving treatment. In Re B (Adult: Refusal of Medical Treatment) (2002) 2 AER 449 the presumption that an adult has full capacity can be rebutted if:
(a) the person is unable to understand the information relevant to the decision, especially as to the likely consequences of having or not having the treatment; or
(b) the patient is unable to use the information and weigh it in the balance as part of the process of arriving at a decision.

Ms B was a competent but paralysed, ventilator-dependent patient, and she won the right to have the ventilator turned off. Although the switching-off had to be performed by a doctor, and this is an act intentionally causing death, the law characterises this as an omission because it amounts simply to a cessation of the ongoing treatment. The doctors’ conduct qualifies as lawful "passive euthanasia". If the particular doctor invited to omit further treatment has conscientious objections, a doctor who will undertake the omission should be sought. But, in more general cases of necessity, urgent surgery may not be unlawful to preserve life pending any judicial decision. Similarly, when the patient is a minor, emergency treatment to preserve life will not be unlawful (note the power to refer issues of consent to the courts under their wardship jurisdiction).

In death with dignity situations where a patient is incapable of communicating his wishes, a doctor may be relieved of his duty, as the House of Lords recognised in Airedale National Health Service Trust v Bland (1993) AC 789. Here a patient who had survived for three years in a persistent vegetative state after suffering irreversible brain damage in the Hillsborough disaster continued to breathe normally, but was kept alive only by being fed through tubes. It was held that treatment could properly be withdrawn in such circumstances, because the best interests of the patient did not involve him being kept alive at all costs. Lord Goff nevertheless drew a fundamental distinction between acts and omissions in this context:
. . . the law draws a crucial distinction between cases in which a doctor decides not to provide, or to continue to provide, for his patient treatment or care which could or might prolong his life, and those in which he decides, for example by administering a lethal drug, actively to bring his patient's life to an end . . . the former may be lawful, either because the doctor is giving effect to his patient's wishes . . . or even in certain circumstances in which . . . the patient is incapacitated from stating whether or not he gives his consent. But it is not lawful for a doctor to administer a drug to his patient to bring about his death, even though that course is prompted by a humanitarian desire to end his suffering, however great that suffering may be.

Duty to act when contracted to do so

In R v Pittwood (1902), the defendant was convicted of gross negligence manslaughter after he failed to close the gate on a level crossing as he was contracted to do. This caused a train to collide with a hay cart, and the court ruled that "a man might incur criminal liability from a duty arising out of contract."

Also:

Such a duty also arises where a "special relationship" exists. For example:
Emergency workers (police, firefighters, emergency medical technicians, etc.) have a general duty to rescue the public within the scope of their employment.

http://en.wikipedia.org/wiki/Duty_to_rescue