When you are living paycheck to paycheck, what bills should you neglect if you have to?

How does one go about structuring their budget when they are living at the brink of insolvency? Do you just neglect paying on credit cards before giving up anything else? And if you do, how do you sign a lease for an apartment if your credit score is in the toilet?

I'm just curious how people get by. I see a lot of people struggling and I wouldn't have the first clue on how to adjust my budget, what options aside from family to find money, or anything else like that.

I'd love to hear from people who are in or have been in that situation.