They are just Rhizoids, which are rootlike extensions that absorb water, food, and nutrients. Unlike in most plants, Caulerpa's do not have a root system. Instead, regularly spaced rhizoid descend vertically from the stolons. They can be few centimeters long, these stuctures branch up into extremely thin filamentous rhizoids. They can also penetrate through the substrate and thus stabilizing the algae. Sometimes you just don't see them or there is less of a need for them thus less of them.