Maybe they like gambling?
Judging by her character and drive to succeed (she emailed 1000+ angel investors, is starting her own business, etc) I could see her occupying a fairly high wage job, in the $50,000 - $80,000 range, if we take a mid point, that's about $65,000 per year for 7 - 8 years.
$65,000 * 7.5 = $497,500 / 10 = ~$50,000.
Assuming that's true, they only stand to lose half - if her idea succeeds however, they could make millions.
I would assume the investor isn't hard up of cash, so losing $75,000 would be a drop of water in the ocean, but making a few million would probably be a nice bonus.
This concept is basically angel investing with some risk mitigation (if the business idea doesn't turn out, but the founder goes on to create another business or get a high-paid job as a non-founder, you get some money out of it), but with a much lower reward.
The lower reward is as follows: A typical angel investor might get, I dunno, 5% equity in a company. In the case of this deal, the "angel" gets 10% of the post-tax amount of the equity that the founder keeps and turns into money.
Which is AWFULLY rough! I mean, suppose that the founder maintains 30% of their company, and then converts all of that to cash, and gets hit with only 15% long-term cap gains, all in ten years. So the angel's effective equity share of the company is .3 * .85 * .1 = 2.55%.