Cryptographically secure PRBGs and the previous-bit test
If you only have a subsequence of the output that does not include the first bit, then the bits of your subsequence can be labeled $b_0$, $b_1$, $\dots$. The bits of the overall sequence from which they are taken would then be labeled $\dots$, $b_{-1}$, $b_0$, $b_1$, $\dots$.
In other words, you're not necessarily starting the labeling of the bits at the beginning of the generator output, but rather at some later point. In that case there is a previous bit, and the previous-bit test applies.