For this one, it’s a numerical issue. I’m not in front of a computer, but when you have a chance, could you try evaluating the log of the inverse cdf of the negative binomial distribution evaluated at 2000 with parameters on the the order 1 (it can even be with both parameters 1)? In Stan, this results in -inf.
The default initialization is uniform -2 to 2 on the unconstrained scale. Since both variables are declared with lower bound at 0, it’s an exponential transform to go from the unconstrained to the constrained scale. See the chapter on transforms.