Excellent questions, Polyocho.  I have no informed answers, but perhaps I can advance the conversation with some guesses.

1. In the US, the "private equity funds" you've been looking at are known as BDC's, and follow certain criteria such as issuing public stock and returning almost all of their ROE to investors.  In the current economy, neither borrowing capital nor issuing more stock is easy to do, so it's hard to keep business going.  BUT... I would never buy these for capital appreciation; they all have humongous dividends, which is their attraction to investors. If they are paying dividends, they still work, even if (or especially if) the stock price is cheap. 

2. In light of #1, there's no proof that anyone is losing anything--yet. We don't know if Yale is still putting a lot of $$ into private equity. More essentially, it's doubtful that their private equity investments are limited to public companies. Large institutional investors can place their bets with venture capital firms which have NO public exposure. Surplus cash is exactly what is in demand in this situation, and I'm sure they don't lack for effective niches to utilize it. 

3. BDC's flourish, I imagine, when it's easy to start new businesses--that is, in a growing economy; and, when credit is cheap. Not now, obviously. 

Aalan