Can a context-free grammar include "dead states" from an automaton, such as
$$G = \big(\{a, b, c\}, \{A, B, C\}, \{A\to aB, B\to b, B\to C, C\to cC\}, A\big)\,?$$
The production rules $B\to C$ and $C\to cC$ will loop forever and never generate a word. Is this allowed or MUST production rules end with an terminal at some point?