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This work continues and substantially extends our recent work on switchingdiffusions with the switching processes that depend on the past states and thattake values in a countable state space. That is, the discrete components of thetwo-component processes take values in a countably infinite set and itsswitching rates at current time depend on the current value of the continuouscomponent. This paper focuses on recurrence, positive recurrence, and weakstabilization of such systems. In particular, the paper aims to providing moreverifiable conditions on recurrence and positive recurrence and related issues.Assuming that the system is linearizable, it provides feasible conditionsfocusing on the coefficients of the systems for positive recurrence. Thenlinear feedback controls for weak stabilization are considered. Someillustrative examples are also given.

Recurrence for linearizable switching diffusion with past dependent switching and countable state space