Borrowing money to buy $60k private stock in a company that just laid you off sounds like a really bad plan.
Sure, that could be a big winning bet, but being that she doesn't even have the money to buy the stock outright means she doesn't have the margin to make that bet.
Sure, the new management COULD be put in place to clean things up to go public. They could also be arranging things for a bankruptcy, or generally be inept and flounder around and ruin the company.
Bottom Line, even if the odds are VERY GOOD that she could hit a big payday, throwing her last $30k in liquid assets as well as $30k of debt after that bet is IMO a very foolish position. If she were my SIL, I would advise her in no uncertain terms to hold her cash and move on.