On all architectures unexpected things can happen which throw the pipeline and funcitonal units and all internal state into a pickle. Somehow the normal flow is suspended and must be continued later. This can happen through interrupts, branch predictions or normal reorders on out of order architectures. The Mill is not out of order, but normal calls there can present small temporary context changes just as interrupts (and interrupts are just unscheduled calls on the Mill). There are several strategies to return to the state before the interruption, all usually called replay.
Result Replay is used on the Mill. Since all interruptions introduce a new belt context in the form of a new frame, all new operations drop their results in their new context (i.e. belt slots), while the already issued operations all finish and drop the results into their old contexts. This happens all via belt slot tagging/renaming with frame ids. On return to the previous flow, all results are presented as if there never was an interruption. It may have been necessary for the spiller to intervene and temprarily save and restore some results for that to happen.
Execution Replay is used on pretty much all major hardware. When an interruption occurs all results and temporary transient state is thrown away, the issued instructions and arguments are remembered though, and on return they are reissued. This can be quite expensive on longer pipelines and with lots of complicated instructions.