Specifically this part:
Any funds you received after this will have been stolen by your partner.
If we are not able to detect te cheater peer, we only get the funds that were allocated by the commitment transaction broadcast by the cheating peer, right? So, if this is correct, what are this "any funds I received after this will have been stolen by your partner"??
Here's an example: you are A and your channel partner is B.
- B opens 1BTC channel towards A
State 0: A
- --- B [1]
[1] B sends A 0.1BTC
State 1: A
[0.1] --- B[0.9]
[2] B sends A 0.2BTC
State 2: A [0.3] --- B[0.7]
If B now broadcasts channel state 1, you will lose
any funds received after this, i.e. the second 0.2BTC payment. In the meantime you may already have shipped some goods or provided a service, so those 0.2BTC are considered to have been 'stolen' from you.