How big were your cuts? From the sounds of your post I would think they were small, and the garment bag/lingerie bag could be a good solution for you. I don't often wash anything smaller than a fat quarter.
How did you lose the fabric, was it so tangled you were able to untangle it? That stinks. :( Unless you have like ten yards of fabric it helps to wash on a getle cycle and you may only need 15-20 minutes drying time in a hot dryer. I try to keep it minimal because the longer you let them dry all those wrinkles set it and are harder to remove. You can usually spray out with a little water or best press any wrinkle from the dryer. Also when I pull my fabric out of the washer I snip threads and sort of shake out each piece of fabric before tossing into the dryer. If you toss that tangled ball into the dryer it will come out a tangled ball of wrinkles! Lol*