No bid - is this possible?

and another girl is complaining that she didn't get a bid, but signed a MRABA so she can't do open bid or rush for a year.

It’s rare but it can happen, however second girl might b misunderstanding the situation. Long explanation but since I’ve heard a lot of people ask. After pref night you sign a form listing the chapters you will accept a bid from, in the order you prefer. If you only have one chapter and you say you will take the bid, you are guaranteed it unless that chapter has a risk management problem with you. If you have two chapters and say you will accept a bid from both of them you are more or less guaranteed a bid to one, but it may not be your first choice.
Where people end up without bids is when they go to two chapters, but “suicide bid” - say they will only take a bid from one. Basically every sorority can take up to whatever quota is- this year it was 80. But, if someone maxed out their options and isn’t high enough on the bid list of one or both of the chapters they preffed, panhell will let chapters take them as a freebie even if it means going over quota. If you suicide bid, you don’t get that guarantee. So if you were high on your chapters list you will get the bid, but you wont get that protection of being added as an addition if you don’t.
For the second girl- That form you sign on pref night is the MRABA. If you sign it that you will accept a bid from either one or two chapters, but you don’t like the bid and don’t want it, you’re done until next formal rush. But, if you suicided and didn’t get offered a bid, or if you put down two options but got a bid from neither (rate but it happens) you can still go through informal.
TL/DR: yes people can end up without bids but usually only if they suicide rush. If you sign the form, but truly don’t get a bid, you can do informal. Hope this helps! Total is artificially higher this year since the school wants bigger chapters, so I expect pi phi to do it for awhile, and chio and likely tri delt to take at least a few since they were both right near the old total last year.