If you are not on welfare, you are entitled to emergency assistance if your health or welfare is in danger. You can get two weeks worth of assistance before your regular application is processed and without going through the usual hoops. If welfare tries to make you get documentation or otherwise delays your application for emergency assistance, call OCAP or a legal clinic.
To qualify for emergency welfare, you must have tried everything to get other money, including by using assets and credit. You also have to show that if you don’t get the money you or your family’s health will be in danger (including loss of housing, loss of heat, not having any food) or that your kids won’t continue to be able to live with you if you don’t get the money.
However, you should know that, while it is the law to give out emergency assistance, it pretty much never happens. It is likely though, that you could get a quicker appointment.