I have a son who's a year younger than your friend's daughter and has both social anxieties and related potty problems as well. Do I have the solution to this problem? H**l no. But I do have one very strong opinion about this little girl's situation.
I honestly cannot believe that a preschool is SUSPENDING a socially anxious child for "accidents." I mean, if a child didn't have social anxiety going into a situation like that, she'd have it coming out. Please forgive me for speaking so strongly, but these actions on the part of the school sound profoundly irresponsible and deeply, fundamentally unkind. Just so I can be super-clear, socially anxious people have oversensitive "shame meters." Using a shaming method like suspension over an issue that this child obviously cannot control is -- well I'll just say it -- abusive. If someone ever did that to my son, not only would I take him out of the school that minute, I'd be talking to a lawyer.
Okay (M. takes deep breath, tries to calm self). Wherever your friend lives, there have got to be other preschool options out there. I cannot recommend this strongly enough. Please suggest that your friend look for a new preschool, and sit down with the director and the teacher before enrolling her daughter. The right preschool should make accommodations for this. They can, for example, assign one adult, perhaps a teacher's aide, to be the little girl's "friend." It's likely to be a lot easier for your friend's daughter to signal to one person rather than raise her hand in front of the whole class. It also sounds within-reason for the mom to be able to drop this little girl's potty off with her daughter and pick it up with her. Finally, putting the social issue slightly aside, it sounds like there are a number of potty-related issues here: fear of pooping, fear of using an unfamiliar potty, fear of letting people know. I think it might make the most sense to address them one at a time -- first poop, then telling people, then the "big toilet." And new school. Please, new school.
Finally, forgive me. I realize that I sound crazed and fire-breathing in this post. I'm not, I mean I'm not like that normally: read my past posts. It just hurts my heart to hear about a child being treated this way.