  In this work, we conduct a study regarding the thermodynamic evolution and
the phase transition of a black hole in a finite spherical cavity subject to
the generalized uncertainty principle. The results demonstrate that both the
positive and negative generalized uncertainty principle parameters $\beta_0$
can significantly affect the thermodynamic quantities, stability, critical
behavior, and phase transition of the black hole. For $\beta_0>0$, the black
hole forms a remnant with finite temperature, finite mass, and zero local heat
capacity in the last stages of evolution, which can be regarded as an
elementary particle. Meanwhile, it undergoes one second-order phase transition
and two Hawking-Page-type phase transitions. The Gross-Perry-Yaffe phase
transition occurs for both large black hole configuration and small black hole
configuration. For $\beta_0<0$, the Gross-Perry-Yaffe phase transition occurs
only for large black hole configuration, and the temperature and heat capacity
of black hole remnant is finite, whereas its mass is zero. This indicates the
remnant is metastable and would be in the Hawking-Page-type phase transition
forever. Specifically, according to the viewpoint of corpuscular gravity, the
remnant can be interpreted as an additional metastable tiny black hole
configuration, which never appears in the original case and the positive
correction case.
