If the business is an incorporated entity, nobody pays for the debt, rather, the company's properties are realised (sold/liquidated) and the proceeds used to settle the creditors in order of preference, paying the ordinary shareholders last. The reason for this is that the company by being incorporated, saperated ownership from management. hence, personal assets will not be touched in event of debt.
If on the order hand, the business is not incoporated, the sole proprietor(s) will be responsible for the debt incuured by the business.
I hope this answers your question?