Syndicated Loans Terminology - Borrower & Sponsor
It sounds like you're talking about a leveraged buyout. In these transactions, a private equity firm (or sponsor as you call them) will acquire an operating company. The debt for the acquisition - raised via the capital markets - will reside on the target company's balance sheet. This debt will be used to pay the previous owners (another PE firm, founders, etc.. whoever owned the company previously). The PE firms will never take debt onto their own balance sheet, and during the course of ownership often raise additional debt on the company to pay themselves dividends.