It's a weird example, but what about

  a 1
  b 101

?

It is neither prefix-free nor suffix-free. Yet every occurrence of 0 corresponds to an occurrence of b.

However, this is obviously inefficient. So I guess the question is whether there's an optimal code which is neither prefix-free nor suffix-free.

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EDIT

I did some googling and found this webpage https://blog.plover.com/CS/udcodes.html where the author gives the following example of a uniquely decodable code:

  a 0011
  b 011
  c 11
  d 1110

I guess this is "almost" prefix-free since the only prefix is c of d. If a message starts wiht 1, you could find the first 0 and then look at whether there's an odd or even number of 1's. So I think I can see how it's uniquely decodable. However, my crypto knowledge is too rusty to remember how to show whether this is an optimal code for some probability distribution.