I got a fish-and-pickled-cabbage soup the other day at a Szechuan restaurant that had these things in it that looked kinda like this. They were translucent off-white, about 2 inches long, and maybe an inch across. They had a light but chewy texture, and at first I thought it was some kind of tripe. What is this stuff?
From your description, if it isn't tripe, then it is probably Bamboo Fungus. This is often used in soup an other dishes and has a neutral flavor. The texture can be from soft to slightly crunchy depending on the length of cooking.
From your description, I (had thought at first - see below) that was indeed a form of tripe, sliced into convenient strips:
This is known specifically as "honeycomb" or "pocket" tripe, and is made from the second chamber of a cow's stomach, anatomically called the reticulum. It and other varieties of stomach are fairly common in traditional Szechuan cuisine.
EDIT: Well, I thought that I had it for sure, but I think erichui's answer is actually correct.