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We present a detailed study of fossil group candidates identified in "Last Journey", a gravity-only cosmological simulation covering a $(3.4\, h^{-1}\mathrm{Gpc})^3$ volume with a particle mass resolution of $m_p \approx 2.7 \times 10^9\, h^{-1}\mathrm{M}_\odot$. The simulation allows us to simultaneously capture a large number of group-scale halos and to resolve their internal structure. Historically, fossil groups have been characterized by high X-ray brightness and a large luminosity gap between the brightest and second brightest galaxy in the group. In order to identify candidate halos that host fossil groups, we use halo merger tree information to introduce two parameters: a luminous merger mass threshold ($M_\mathrm{LM}$) and a last luminous merger redshift cut-off ($z_\mathrm{LLM}$). The final parameter choices are informed by observational data and allow us to identify a plausible fossil group sample from the simulation. The candidate halos are characterized by reduced substructure and are therefore less likely to host bright galaxies beyond the brightest central galaxy. We carry out detailed studies of this sample, including analysis of halo properties and clustering. We find that our simple assumptions lead to fossil group candidates that form early, have higher concentrations, and are more relaxed compared to other halos in the same mass range.