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Complex questions in retrieval-augmented generation require evidence spread over several documents, and an answer is reliable only when the retriever finds all of it. Chain embedding retrievers collect such evidence step by step, re-encoding the question together with the passages retrieved so far, and we find that they are already strong: trained only on gold histories, a small chain embedding retriever that calls no language model outperforms graph-based systems and is competitive with a search agent. This training, however, leaves a gap. At test time the retriever conditions on its own retrievals, which soon contain mistakes: by the third step, about half or more of the states it visits hold a wrong passage, and these passages lower its chance of retrieving a missing gold passage well beyond what the difficulty of the states explains. We propose on-policy state training, which trains the encoder on the states it reaches itself. At every epoch the current encoder retrieves chains for the training questions; each state it visits, including those built on its own mistakes, is labeled with the earliest gold passage still missing while the other missing gold passages are masked, so that no correct continuation is penalized; and the encoder is updated contrastively on these states mixed with teacher-forced ones, so that its training distribution follows it as it learns. The resulting retriever retrieves complete evidence more often than teacher-forced training and the systems we compare, and it transfers without further training to harder long-chain variants of HotpotQA and 2WikiMultiHopQA that we construct. On the same states, it recovers from its own mistakes far more often, and controlled comparisons attribute the gain to training on the states the encoder currently reaches.