Signal detection theory: How to calculate c' when d' is 0?
As you mention Macmillan and Creelman, they talk about 3 types of bias: c, c', and beta. As I said in this answer it normally does not matter which one you use since they are pretty easy to switch between. When d' is zero, then c' and beta are no longer as informative as c. I would suggest reporting c, possibly along with c', in this case. Alternatively, you could report hit and false alarm rates. If you only report c' and d', you will not be telling the whole story.