What happens when an emergency occurs? Where does the company get funds to replace vital broken equipment, pay for a worker to take paid sick leave? Or a number of other emergencies?

Okay... but that doesn't come from profits. So long as you've got the revenue you can budget for that. Those are just costs of doing business. Unplanned costs can be carried on credit cards or you try to work out a payment plan with whatever you're needing to call on to deal with an emergency.

How does the company expand operations? Where do they get the funds to hire and train additional workers? Open a new branch? Etc?

Why would a company expand operations when they don't have revenue? If you're not making more than "break even" money... why would you need to hire new workers. If you're not planning on expanding.... Businesses don't "have" to grow bigger than what they already are. If you're just wanting to make jelly in your kitchen and sell it to your neighbors, you aren't looking to rent an industrial scale kitchen and hire on a workforce.

Do you take on debt? How do you pay off creditors if you’re breaking even? Do you issue bonds? Do you issue bonds? Then how do you pay the premium?

The same way a person deals with paying for things on debt. You juggle your cash.

If your company is breaking even, then your company is dead. You are one small emergency from insolvency.

Heres a funny story, my partner has been self employed for about 15 years now, doing small farm stuff. The only people who do the labor are ... us. The farm revenue makes enough to keep the farming going to make enough revenue to keep the farm going. Its a rare year that there is a "profit" by the end of the year. Do you wanna know how we pay for things? I have another job that pays me money, and that money is used to pay for things like the electric bill and the groceries that can't be grown outside and the phone bill, etc etc.

Some people, actually just want to do a thing and be able to make some sort of living off of it, even if its a small one instead of create "business" for the sole purpose of selling the business to the highest bidder. I know right? Its mind blowing.