I am reading about Entanglement-assisted Quantum Error Correction Codes from Quantum Information Processing and Quantum Error Correction: An Engineering Approach (Chapter 9) . It is a scheme that allows the usage of any classical error correction code. Furthermore, it uses entangled qubits (ebits) which is the Bell state $\vert \Phi^+ \rangle$. It is assumed to be error-free and shared between the sender Alice and receiver Bob, prior to the start of the communication.
Alice will encode her state $\vert \psi \rangle$ with the help of local ancillary qubits $\vert 0 \rangle$ and her half of shared ebits. She will then sends the encoded qubits over a noisy quantum channel.
The book then states:
Notice that the channel does not affect the receiver’s half of shared ebits at all.
How is that even possible? I thought if one entangled subsystem changes, then the other changes automatically.
Furthermore, consider the following (to make it simple, assume one ebit is used which is shared between Alice and Bob before communication begins). Let us say Alice will send her half of the ebit over the noise channel and a bit-flip occurred, what happens to the other half (Bob's half)?