  Hubble constant($H_0$) tension and tension in the matter fluctuation
amplitude ($s_8$) are fascinating puzzles in cosmology nowadays. Phantom
dynamical dark energy model (PDDE), also known as little sibling of the big rip
is an abrupt event that can happen in the far future evolution of the universe.
Recent analysis of PDDE model based on CMBR data shows that the model is a
potential candidate to alleviate these tension problems. In this work, we study
the background evolution of the universe within the PDDE model. Analysis based
on the SNIa+BAO+OHD data shows that the model is successful in explaining the
late phase acceleration of the universe. Also, the values of the cosmological
parameters predicted by PDDE model are consistent with the values predicted by
the $\Lambda$CDM model. However, most of the phanton dark energy models doesn't
give stable solution in the asymptotic future. In this regard, we address the
dynamical stability of the PDDE model and also test the validity of the
generalized second law (GSL) of thermodynamics. We show that the model is
dynamically unstable and violates the GSL. The model doesn't satisfy the
convexity condition and hence the universe doesn't behave like an ordinary
macroscopic system within the PDDE model.
