In the $x Cdot Y = K$ Model, What Happens to the Price as One Reserve Approaches Zero?

As one reserve ($x$ or $y$) approaches zero, the price of the remaining token approaches infinity, assuming the constant $k$ is non-zero. The constant product formula dictates that to maintain $k$, a small trade in the diminishing token requires an exponentially large amount of the other token.

This extreme price increase effectively makes it impossible to fully drain the pool, a key feature that provides "infinite" liquidity, albeit at an increasingly prohibitive cost.