Discrete sequences in unbounded domains

Discrete sequences with respect to the Kobayashi distance in a strongly pseudoconvex bounded domain $D$ are related to Carleson measures by a formula that uses the Euclidean distance from the boundary of $D$.
Thus the speed of escape at the boundary of such sequence has been studied in details for strongly pseudoconvex bounded domain $D$.
In this note we show that such estimations completely fail if the domain is not bounded.