What is a non-starving policy in reinforcement learning?

In the paper, Eligibility Traces for off-Policy Policy Evaluation (2010), by Doina Precup et al., mentioned the term "non-starving" many times. The specific use of the term was like "non-starving policy" in the context of off-policy learning.

A specific mention of the term

we consider a method that requires nothing of the behavior policy other than that it be non-starving, i.e., that it never reaches a time when some state-action pair is never visited again.

What does the thing look like intuitively? Why is it required?

A non-starving policy is a (behavior) policy that is theoretically guaranteed to visit each state and take all possible actions from each state an infinite number of times, so that to always update $$Q(s, a)$$, $$\forall s, \forall a$$, an infinite number of times. In the context of off-policy prediction, this criterion implies that any trajectory will have no zero probability under a behavior policy. As a consequence, the experience from the behavior policy sufficiently covers the possibilities of any target policy.
An example of a non-starving policy is the $$\epsilon$$-greedy policy, which, with $$0 < \epsilon \leq 1$$ (which is usually a small number between $$0$$ and $$1$$) probability, takes a random action from a given state, and, with $$1-\epsilon$$ probability, takes the current best action, that is, the action with the highest value from a given state, according to the current value function.