Abstract We discuss how one can systematically construct point particle theories that realize the vanishing one-loop cosmological constant without Bose–Fermi cancellation. Our construction is based on the asymmetric (or non-geometric) orbifolds of supersymmetric string vacua. Using the building blocks of their partition functions and their modular properties, we construct theories which would be naturally identified with certain point particle theories including infinite mass spectra, but not with string vacua. They are obviously non-supersymmetric due to the mismatch of the bosonic and fermionic degrees of freedom at each mass level. Nevertheless, it is found that the one-loop cosmological constant vanishes, after removing the parameter effectively playing the role of the UV cut-off. As concrete examples we demonstrate the construction of models based on toroidal asymmetric orbifolds with Lie algebra lattices (Englert–Neveu lattices) by making use of the analysis given in Satoh and Sugawara (2017)