When an agency has decided to close down or let a girl go, is there an etiquette to discussing be with them the possibility of getting one of their former providers contact information? Is it impolite to do so?

If the agency has closed, then you probably won't be able to reach them.

If the agency has let someone go, they are extremely unlikely to want to support her taking clients away.

IF you can get thru to the agency that has shut down, there are ways to ask politely (not that it will work) and impolitely. Avoid the latter.

Follow other agency ads and see if she turns up.  A new review can take much longer, even after she starts at another agency. She might change her name or her look in the interim.

After a while, you can post to the "In Search Of" board or the NY board your ISO. I am assuming that she has a Profile you can post with your ISO request.  If the agency was banned by TER (rather than just a self inflicted shut down), you won't be able to say, "Looking for Mary, formerly of XYZ Agency" and you'll have to be more descriptive.  

Be prepared to just move on.  

Good luck