In this work, we study the merger of two neutron stars with a gravitational mass of 1.4 M⊙ each, employing the Shen-Horowitz-Teige equation of state. This equation of state is a corner case, allowing the formation of a stable neutron star with the given total baryonic mass of 3.03 M⊙. We investigate in unprecedented detail the structure of the remnant, in particular the mass distribution, the thermal structure, and the rotation profile. We also compute fluid trajectories both inside the remnant and those relevant for the formation of the disk. We find a peanut-shaped fluid flow inside the remnant following a strong m =2 perturbation. Moreover, the flow is locally compressive, causing the appearance of dynamic hot spots. Further, we introduce new diagnostic measures that are easy to implement in numeric simulations and that allow one to quantify mass and compactness of merger remnants in a well-defined way. As in previous studies of supra- and hypermassive stars, we find a remnant with a slowly rotating core and an outer envelope rotating at nearly Keplerian velocity. We compute a Tolman-Oppenheimer-Volkoff star model which agrees well with that of the remnant in the core, while the latter possesses extensive outer layers rotating close to Kepler velocity. Finally, we extract the gravitational wave signal and discuss the detectability with modern observatories. This study has implications for the interpretation of gravitational wave detections from the postmerger phase and is relevant for short gamma-ray burst models.