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We investigate the structural parameters and dynamical state of the $2\:$Gyr old open cluster NGC 2506 based on more reliable cluster members. We apply a robust clustering method to calculate membership probabilities for more than 8000 sample stars within $90^{\prime }$ (${\sim}81\:$pc) from the cluster center in the Gaia-DR3 catalogue. Based on the membership probabilities, we identify more than 2500 members (including extra-tidal members) which cover a wide range of magnitudes ($G\sim 9$-$20\:$mag). We find that NGC 2506 has a detectable radius of $R_{cl}\sim 40^{\prime }$ ($36\:$pc), and its members extend up to a large radial distance of at least $90^{\prime }$ ($81\:$pc) from the cluster center. We determine the core and tidal radii of the cluster to be $R_{\rm c}={2{_{.}^{\prime }}69}\pm {0{_{.}^{\prime }}02}$ ($2.4\:$pc) and $R_{\rm t}={48{_{.}^{\prime }}02}\pm {4.84}$ ($43.3\:$pc), respectively, indicating a high concentration parameter of $\log (R_{\rm t}/R_{\rm c})\sim 1.3$ for the cluster. A Gaussian mixture model and principle component analysis are used to investigate the two-dimensional structural parameters of the cluster. We find that NGC 2506 has a near-circular core ($e\sim 0.96$) and a slightly elongated halo ($e\sim 0.87$). In addition, we find evidence for the existence of some extra-tidal members (including some high-mass stars). We also find that some red clump giants inside the tidal radius are located at distances smaller than the mean distance of the cluster, suggesting that they may have escaped from the cluster. Our findings suggest that NGC 2506 is losing its member stars, including high-mass stars. However, no clear tidal tails can be detected around the cluster.