See Simplicity bias in finite-state transducers

You need to be able to loop around the non-coding region, and around the coding region to get non-trivial designability/complexity plots.

This FST shows a good example of an approximately absorbing region with two non-coding states. The fact that the region is approximately non-absorbing, and as there is a cycle outside that region, means we will get variety in output.

FST table:

0 2 1 1 0 1 0 1 1 4 1 0 1 3 0 0 2 1 1 1 2 0 0 0 3 2 1 0 3 1 0 0 4 1 1 0 4 1 0 0 0 1 2 3 4

In this example there is clear bias towards a $000000...$ sequence, as there is an absorbing region made entirely of $0$-noncoding states. However, the rest of the fst does not have any loop, so there's barely any possibility for variety of outpus, and the designability/complexity plot is trivial.

Here is an example of a FST with an approximately absorbing region with non-coding states that is the whole fst.