Imagine if such a planet had a small residual rotation left - any civilization on it would be constantly rediscovering millennia-old sites as previously abandoned regions rotated back under the inhabitable region.
The sort of forced nomadism from "only" having ~1000 years before a location becomes uninhabitable would make for some interesting dynamics. Real estate at the leading edge would be very valuable, potentially with some kind of homesteading dynamic for claiming the land (as nobody has lived there for thousands of years). Also value of land would depreciate over time because it would have an 'expiration date'.
Also, the polar territories would only have to worry about precession, and their land might have a longer expiration date.
But soon the Bright comes, melting the glacier which holds the lake back from the Dark. They can't cross, it's now full of chunks of ice, and they have to get through hostile neighboring lands.
Call it Sunrise.
[0] https://www.reddit.com/r/WritingPrompts/comments/35mgnn/wp_a...