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Living systems at all scales aggregate in large numbers for a variety of functions including mating, predation, and survival. The majority of such systems consist of unconnected individuals that collectively flock, school, or swarm. However, some aggregations involve physically entangled individuals, which can confer emergent mechanofunctional material properties to the collective. Here, we study in laboratory experiments and rationalize in theoretical and robophysical models the dynamics of physically entangled and motile self-assemblies of 1-cm-long California blackworms (Lumbriculus variegatus, Annelida: Clitellata: Lumbriculidae). Thousands of individual worms form braids with their long, slender, and flexible bodies to make a three-dimensional, soft, and shape-shifting "blob." The blob behaves as a living material capable of mitigating damage and assault from environmental stresses through dynamic shape transformations, including minimizing surface area for survival against desiccation and enabling transport (negative thermotaxis) from hazardous environments (like heat). We specifically focus on the locomotion of the blob to understand how an amorphous entangled ball of worms can break symmetry to move across a substrate. We hypothesize that the collective blob displays rudimentary differentiation of function across itself, which when combined with entanglement dynamics facilitates directed persistent blob locomotion. To test this, we develop a robophysical model of the worm blobs, which displays emergent locomotion in the collective without sophisticated control or programming of any individual robot. The emergent dynamics of the living functional blob and robophysical model can inform the design of additional classes of adaptive mechanofunctional living materials and emergent robotics.