The business should have to make up the loss somehow. It could be loss of gp (at the relevant rate, be it labour, magic, etc) or lose some appropriate equivalent.
For example, if it needs more Influence, someone is complaining and causing loss of business. If it needs more Labour, some employees have gone on holiday and aren't working. If it needs more Goods, it's run out of raw materials and can't generate money. Magic might get more interesting, or be irrelevant for something entirely mundane.
It rather depends on the business.
Apologies for the partial necro, but by rules, if you have no capital to lose, you don't lose anything: capital doesn't go into the negative. Gold technically doesn't either, but strictly speaking, you that business can only lose gold they ahve in their possession (so gold on your person doesn't magically disappear unless Plot shenanigans).
The reason for this: attriction is based on the idea of capital (such as goods) falling due to theft, faultiness accidents using it, etc, etc. It's not just some random tax. If there's nothing to lose, it can't go into the negative. So long as nothing destroys the business or interferes with general business, it should not go bust.
That said, there are some blatant holes in how downtime works. Nothing stops houseruling this, but doing so is kind of sucker punching starting business with extra penalties that don't make much sense, so I don't recommend it. Even if your business is only generating gp, adventuring is still far more profitable and you shouldn't have to worry about it breaking things unless you somehow build an entire empire in a metropolis or something (and the realistic counter to that is game plot starts involving said metropolis and business more directly than just the downtime system).