I'm definitely not trying to recommend skipping out on building an emergency fund to everyone just trying to throw out some alternatives for a small subset of individuals. To answer your question, the primary information creditors or lenders look at in loan applications is your credit score. When you lose your job your credit score does not automatically go down. Your score will go down if you begin to miss payments but the idea here is to use the credit score you build up while you had a job to apply for a card(most applications get denied or approved within a week) that has a 0% introductory APR and put your expenses on there during emergencies.
Yes, most creditors will also look at what they call your Ability to Pay(ATP) which is essentially your debt obligations against your income, but this is mostly utilized by the creditors to determine the size of your credit line or CLI's/CLD's(credit limit increases/decreases).
Keep saving for your emergency fund!! While there are alternatives for people with different risk tolerances, if you have to support a family or others, don't risk it.