Worm type bug inside of stick? What is it?
It looks to me like the larva of a case-bearing moth. Despite the common name, the case is made by the larva, as seen here. What you are watching is the larva creeping out, then moving forward, bringing its case with it. Larvae of other moths make cases out of various kinds of hard materials, such as pieces of stick or grains of sand. Have a look at the possible duplicate noted above, which has helpful info.