traveling to Canada without passport/greencard

My wife is a US permanent resident. Her internat. passport is expired and we haven't received her new green card after 18 months of waiting and 2 follow up visits to INS.

She DOES have another piece of paper that INS gave her though. It has a current I-551 stamp and her photo. Can we use this to go to Canada and back?

To give you an asnwer you need to say what this "another piece of paper" is...
In other words, be more specific...

It has no document number on it. It's an additional document I've heard they give out if your passport is expired. They cannot put another I-551 stamp in an expired passport, so they issue this paper card with your photo and new I-551.

Can you at least describe how it looks like? How many pages? Color? US seal somewhere? Any text? What does the text say? etc.
From your short description, it may be a so-called white passport (I have heard that they recently changed the color to green.)
Usually, people on asylum get that, because they obviously can't get a passport from their home countries.
It is also used as reentry permit or Advance Parole travel document.
But, to be sure, you need to provide a better description. I am sure it has some text on it that says what it is. If it is an official document, I am pretty sure it has a document number somewhere.