A hypothesis of absolutely stable strange hadronic matter composed of Λ(1405) baryons, here denoted Λ * , is tested within many-body calculations performed using the Relativistic Mean-Field approach. In our calculations, we employed the Λ * Λ * interaction compatible with the Λ * Λ * binding energy B Λ * Λ * = 40 MeV given by the phenomenological energy-independentKN interaction model by Yamazaki and Akaishi (YA). We found that the binding energy per Λ * , as well as the central density in Λ * many-body systems saturates for mass number A ≥ 120, leaving Λ * aggregates highly unstable against strong interaction decay. Moreover, we confronted the YA interaction model with kaonic atom data and found that it fails to reproduce the K − single-nucleon absorption fractions at rest from bubble chamber experiments.