I'll touch on what hasn't been explicitly said. In the past 10 years, it has become very popular, particularly on campuses with large numbers of PNMs and chapters to use the release figure method (RFM). The purpose of the release figure method is to place the maximum number of PNMs. Certain chapters ("popular" ones---ones that a high percentage of PNMs would opt to return to if invited) are
forced by the College Panhellenic to cut a high percentage of PNMs after the first round. Other chapters will make the majority of their cuts at different points in recruitment.
I've read recruitment stories from before the RFM was used. It was fairly common for a PNM to be invited to every (or almost every) chapter after the first round. So, of course, the PNM has the power to cut whichever chapters she wants, and usually it's the "low-tier" chapters that get cut in such a situation. Meanwhile, the "popular" chapters are inviting back tons of PNMs that they have no real intention or ability to pledge. Not using RFM on a big campus will usually guarantee a big discrepancy in size among chapters (ie "low tier" chapters don't make quota), and a lot of PNMs who get cut out of options later in recruitment because they opted to cut chapters where they had a realistic shot at a bid (lots of unmatched PNMs). VERY often, women will return to chapters that they didn't like after one or two rounds (ie. would have cut them if allowed) and find that it is the place for them.
Now, about "popular" chapters and their cuts. I will never know how any other chapter does membership selection but my own (and that's in a limited time frame), but I can speculate that because they have to make the biggest cuts after the first round that there isn't always a "reason" or there is a silly reason that you talk yourself into feeling good about because Panhellenic is forcing you to make these drastic cuts. There can be legitimate connection between a PNM and an active, but the PNM is cut simply because they have to make a certain amount of cuts, and there were more PNMs that they liked better for one reason or another. This is a problem that "popular" chapters face: how to find what you are looking for after only one party. They can choose based on whatever criteria they want, but they still must make those cuts.
Also, about suiciding. Your daughter wasn't "forced" to suicide; in fact, she was probably encouraged to list all of her preference chapters. Some campuses also have a "guaranteed matching" policy--if they have at least one preference invite, and rank all preference chapters they attended, Panhellenic will guarantee they will be matched to one of those chapters. If a large number of PNMs suicide, there will be more unmatched women, so it is discouraged. Women who suicide can and do get bids often, but it makes the PNM question, "If it came down to my second or third choice, would I rather have them or not be Greek?"
Even if your daughter feels she would have been a better fit elsewhere, encourage her to try to like her group she is pledging. She won't have a chance to pledge anywhere else until next year anyway. She might just find that she couldn't imagine herself anywhere else.