Once, I had booked a train from Germany to Switzerland. Due a train strike, Deutsche Bahn informed us our tickets could be used on different dates. I indeed travelled on a different date, but the conductor on the Swiss train said my ticket was not valid.
Another time, I booked a Sparpreis (saver fare) from Switzerland to Germany. The direct train from Zürich to Frankfurt was cancelled, so Deutsche Bahn told me the Zugbindung (requirement to take indicated train) was lifted. I took an earlier train, but the conductor on the Swiss train again said my ticket was not valid, because there was a replacement train for the Swiss part that I had to take (see also If my train is cancelled and replaced, must I take the indicated replacement train when I have a Sparpreis ticket?).
In both cases the conductor let me travel anyway, but with less luck I might have to pay a fine and a replacement ticket.
What are my rights on international journeys between Germany and Switzerland, when Deutsche Bahn informs me that, for whatever reason, I have more flexibility than I normally would have?
If I have a Sparpreis and I am delayed from Germany to Switzerland, can I take a later train within Switzerland?
If I have a Sparpreis and I am expecting a serious delay from Switzerland to Germany, can I take an earlier train within Switzerland?
If there are strikes or other severe disturbances in Germany and I am adviced (by Deutsche Bahn) that I can travel on a different date, does that apply to the Swiss part of the journey as well?
Is this officially written down somewhere, that I could refer to if I have a discussion with a Swiss conductor?
¹This happens often: when the train from Germany to Switzerland is delayed, the Swiss railways run a replacement train from Basel (departing on schedule) and the German train is cancelled beyond Basel. Unlike in Germany, trains in Switzerland tend to run on time.