If I understand correctly, their money stuck inside the PE funds/companies, so they use this "securitization process = bond issuance" to transfer the risk of the PE (private equity) asset class to the public. They collect the lump sum of money (at present value immediately at bond IPO), and in return promise to pay the (periodic stream of) bond coupons (at approximately equivalent interest rate of a corporate bond) and eventually the principal at maturity back to the "bond" buyers.
So if I understand correctly, the bond buyer assumes private equity risk and accepts corporate bond interest rate as reward in exchange. The bond issuer keeps its private equity reward (because this reward is never (fully) transferred to the "bond" buyer) and reduces its own risk in its PE investments.
To clarify a bit, as BBCW has pointed out, it is a structured finance instrument, which is not entirely the same as a corporate bond.
A corporate bond is issued by a company in operation, whereas for structured finance it is more akin to a group of investors who want to invest(in the broadest sense of the word) but want to borrow money from you to do so (in addition to some of their own). The money you lend them is "collateralized" by that specific group of investments.
As a result, there are different "tranches" in the structure of the combined money (yours and the investors) which denote the seniority and yield you will get. Naturally, the more senior you are, the lower your yield. However, this also means if that group of investments go belly up, you will be earlier in line to get your money back due to your seniority.
The earlier-mentioned investors usually form the equity tranche of the structure, which is usually the lowest level in seniority. In the case of Astrea V, about 55% of the entire structure is equity. If there are any losses, they will be the first to lose and but the debt obligation to you remains unchanged.
So in a simplified way of looking at it (ignoring some other specific details), if you are a Class A-1 holder of the "bonds", it will take a write-off of more than 50% of the total investment value before you suffer any loss. On the other hand, the equity tranche (the investors) will lose almost everything in such a scenario.
However, if the investments do exceedingly well, you will get back your money in full. But, the equity investors will be laughing their way to the bank. They may even have made several times of what they originally put in. This is because they keep any upside in the investment, while you only get back what you lent them.
So you get less risk, but also less reward. They get more risk, but also more reward. Life is fair eh?
But whether it is because some their money is "stuck" and they want to cash it out by getting investors like us to lend them money(leveraged recap) or they simply need more money to invest cause its cheaper to borrow rather than put up their own money I don't know. Maybe some PE guys will know better for this case.