There is an ending in which your family dies. I want to get this ending as fast as possible. Can I just turn heating off and not buy food, or will I die myself?
You cannot die from cold or hunger in Papers, Please. Only your family members can.
When you don't pay the heating or food bills, your family members get cold and/or hungry. This can cause them to get sick, prompting you to buy medicine for them. If you don't, they will get very sick and die.
If you just want to kill them all, never pay the heating or for food. It will only take a few days. If all your family members die, the game ends.