This bug was found on the wall of my closet in Seattle, Washington. It has been around 40-50°F lately, and it is winter. It looks like a tiny, brown, fuzzy stick/twig, but there is a hole through the middle of it. A tongue kind of thing comes out of the hole. The tongue thing is clear/tan and has a brown tip. The tongue is how it moves around and it looks like the tip sticks to the ground, and then it pulls the rest of its body/the stick part forward from there. It doesn’t seem to like it when light is shined on it (like from a phone flashlight) and goes back into the twig part when light gets shined on it. The twig part doesn’t seem to move on its own. The twig when the tongue is inside is about 0.5 cm.
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.