You need to take the phrase as it stands (i.e., not looking at "off-chance" on its own); then (OED): "on the off-chance : just in case," i.e., simply für den Fall, dass.

Yes, sorry, my OP may have been a bit garbled, especially if you see "off chance" and "on the off chance" as two separate phrases. I only ever use "off chance" in the phrase "on the off chance", which, to me, refers to an unlikely possibility. Various online dictionaries confirm this. Interesting to see that the OED defines it as "just in case".

https://www.oxfordlearnersdictionaries.com/de...

on the off chance (that)

because of the possibility of something happening, although it is unlikely

I didn't think you'd be at home but I just called by on the off chance.

She scanned the crowd on the off chance of seeing someone she knew.

I called in at the office on the off chance that you would still be there.

https://dictionary.cambridge.org/dictionary/e...

on the off chance

hoping that something may be possible, although it is not likely:

I applied for the job on the off chance that they might like me, but I didn't seriously expect to get it.

https://www.collinsdictionary.com/dictionary/...

on the off-chance

PHRASE

If you do something on the off-chance, you do it because you hope that it will succeed, although you think that this is unlikely.

He had taken a flight to Paris on the off-chance that he might be able to meet Francesca.

...an American visitor who had turned up on the off-chance of catching a glimpse of the princess.

I was just interested to hear how others used it.

I’m afraid I wasn’t being at all precise at the end of #3 when I wrote “tends to be my most frequent use of it.” That’s not true.

For the OP the sense “in case” would work.

My own most frequent (exclusive?) use of “on the off-chance” has been in sentences like “I called by on the off-chance [but, e.g., they weren’t in],” where there’s little or no sense of the likelihood involved but simply the idea of leaving it to chance; more or less synonymous: “I called by hoping they might by chance be in” (not “ … on the unlikely chance they might be in”).

Have I been using it incorrectly all my life? Is there a BE/AE distinction?

This example from online I would say is typical:

'It was very good of you to call by on the off chance.' 'It was on my way home,' he said expressionlessly, his eyes on the traffic. 'Where do you live?' She kept her ...

Interesting, Bion, thank you. Your understanding of the phrase is clearly similar to Pat Barker's, so you're in very good company.

I would also use it in sentences such as "I called by on the off chance they might be in", but would intend that to mean "... on the unlikely chance".

I guess it's the sort of phrase where people would be unlikely to ever notice that they were talking (slightly) at cross purposes. If someone told me they had dropped by on the off chance that I might be in, and they meant "in case" but I understood it as "in the unlikely event", neither of us would be any the wiser afterwards. The only reason it jumped out at me here was that it is used in reference to something that does have a relatively precise probability attached to it.

Having since finished the book, there is a very similar passage towards the end:

I'd heard [Agamemmnon's] plans for Troy, his and Nestor's. Every man and boy killed – and that would include my brother-in-law – pregnant women to be speared in the belly on the off chance their child would be a boy, and for the other women, gang rape, beatings, mutilation, slavery. A few women – or rather a few very young girls, mainly of royal or aristocratic birth – would be shared out among the kings.

OT: I really liked it. (Much more than the new Robert Harris, which I read afterwards.) I will certainly be reading more Pat Barker. Is there one you would particularly recommend, hm? I know you're a fan. I was thinking I might try Border Crossing next rather than dive straight into the Regeneration trilogy...

I think hm – us comes close to putting her finger on it in her second paragraph (#4). Assuming that Barker is using it in the (BE?) sense of “in case by chance,” then to use, highly unusually, what’s generally used in nondescript situations (“I called by on the off-chance of finding him home”) in the context of war and killing gives something offhand to the action, i.e., the choice of language reflects back on the killers’ attitude—hm – us: “it seems to convey someone’s dismissive point of view” (although I’d disagree that it has to do with “disregard … for statistical probability”).

#7 I guess it's the sort of phrase where people would be unlikely to ever notice that they were talking (slightly) at cross purposes.

Yes.