If you encode S = "abaaaaaaac" with c acting as EOF character, the last intervals ist [0.6520795944 0.656777216)
0.10101$_{2} = 0.65625$ is in that interval and has 5 Bits, whilst the entropy of S is 0.92, so you would need atleast 9.2 Bits to encode it. (The 0. in front is only for this explanation, not actually necessary in the algorithm) The correct encoding would be 0.10100111111$_{2} =0.65576171875$, which is a prefix code, but you can still correctly decode S with 10101? But if you add a 1 to it, you get 0.101011$_{2} = 0.671875, which is not in the interval anymore, so it isn't a prefix code.
"It is not necessary to transmit the final interval, however; it is only necessary to transmit one fraction that lies within that interval. In particular, it is only necessary to transmit enough digits (in whatever base) of the fraction so that all fractions that begin with those digits fall into the final interval; this will guarantee that the resulting code is a prefix code." This is copied from Wikipedia.