Please re-read the title of this with an emphasis on the YOU. This is not how-to run, but about how you operate, function, work in a business with no money. I had a discussion recently with someone facing this problem in their company, and he said, "You should write about that on your blog." It was an overdue push, given I've been suffering from a combination of writer's block and busy-ness of late. So, let's have a go.
I believe the example that might be most salient is that of a business that begins in parallel with a fund-raising effort. Many one-person businesses knowingly start on a shoestring, but larger efforts often begin with partners (both business partners and supporters offering their services) while outside funds are being sought. Things typically start with a flurry of activity and energy. The plan often includes optimistic assumptions about how quickly funds can be raised and time to revenues. As the reality establishes itself, the energy will cycle, but the need for activity remains and increases. On top of this, the needs of the business change quickly as more is learned about the business, feedback from investors, etc. Meanwhile, those involved in the business learn a lot about their partners and how they work. Herein lies the lesson.
Even at this point in my description, I guarantee that you have assumptions about how you and any logical person would function in this environment. There are two challenges in this. First, you do not know how you will function until you are in the situation. Second, I guarantee you that your assumptions about how "anyone in this situation" would act are not going to be true of your partners.
Let's get specific for a minute. After you have gone six months beyond your initial projections of when funding would be closed, how do you work with suppliers on work you need from them when you haven't paid their last two invoices? Do you use your credit card to buy that plane ticket for that industry meeting that will generate some good leads, but no sales for a year? Do you call your old boss or start looking for "a real job"? Does your spouse tell you to get "a real job"?
Many people will put heads down and plow ahead to get done what needs to get done, but the reality of money is the big strain. Some people become strategic and want to retrench or determine a new plan of attack, but the cost is time. Some people will curl up in the fetal position and need to be cut loose.
If we assume success for the purpose of this discussion (which I have seen perseverance often yields, although in a different form than you may have sought), you will also be amazed at the difference in how people operate after the first funding obstacle is cleared. Lifting the burden of running a business with no funding is a relief that can elicit a dramatic change. Some people view it as having been living a lie. Those who put their head down with less (or no) regard to money, will often show little or no change. But within a business, it is safe to assume that some partners will behave dramatically differently. This has an impact on the overall business, and this cannot be underestimated.
As is typically the case in my musings here, I will tell you that there is no right answer, but I am telling you that this will happen to many a new business. Consider your own situation and how this inevitable reality will impact you. Then consider your partners and the impact on them. It all adds up to an impact on your business, and it can be the difference between your surviving this trial or not. Good luck!