The fabrication of multifunctional materials with tunable structure and properties requires programmed binding of their building blocks. For example, particles organized in long-ranged structures by external fields can be bound permanently into stiff chains through electrostatic or van der Waals attraction, or into flexible chains through soft molecular linkers such as surface-grafted DNA or polymers. Here, we show that capillarity-mediated binding between magnetic nanoparticles coated with a liquid lipid shell can be used for the assembly of ultraflexible microfilaments and network structures. These filaments can be magnetically regenerated on mechanical damage, owing to the fluidity of the capillary bridges between nanoparticles and their reversible binding on contact. Nanocapillary forces offer opportunities for assembling dynamically reconfigurable multifunctional materials that could find applications as micromanipulators, microbots with ultrasoft joints, or magnetically self-repairing gels.