The paper used today is not like it use to be. I think it will separate and be little balls dried to the fabric.
I have started to use Stable Stuff. You leave it in and when washed turns to a very thin layer of poly, not enough to add thickness. Walmart sells a wash a way stabilizer and I bought a 25 yard bolt of it when it was on clearance price of $1 per yard. Always keep an eye out for clearance prices on items you don't think you will ever use.

My guess is that it would be the same as when you wash a shirt or pair of pants with a Kleenex tissue still in the pocket: shredded, matted, hard chunks that stick to the fabric.

They also have some type that wash away so If I was going to do one like that I would use a wash away kind similar to a stabilizer

If the paper is not water soluble I would not recommend it. Have you ever left paper in your pockets and washed it? Not pretty.

A shop near me sells this stuff. It is preprinted sheets for several different patterns. It stays in the quilt.

http://farmlandquilting.net/stable-piecing/

DebraK and MQ2-- Just make sure you get all the pieces in the trash can before you go to bed, or the cat will think you left it there just for her. Ask me how I know.

I stitch the lines before I sew.... no thread.... so it makes it easy to fold back when I'm lining up the pieces of fabric and easy to remove the paper. I know that is an extra step but it saves so much when it comes time to remove the paper that it's worth it to me.

years ago ladies would leave the paper in because it would add an extra layer of warmth.

That's paper piecing. Foundation piecing is just the paper foundation, no pattern needed. Mostly is is used for string quilting or English paper piecing. Foundation usually needs a backing of some kind to keep the strips and pieces anchored. Not stitching on the paper would defeat the purpose.

What about Ricky Tim's stable stuff? It can stay in the quilt and softens when washed.