Suppose that someone was spelunking in a French cave when a small earthquake caused a passage to open. That passage leads through a narrow constriction and emerges in a different part of the cave complex... ten years in the past. Each... let's say counter-clockwise trip through the loop takes one back what is apparently ten years. Each clockwise trip brings you ten years forward up until the present, at which point, if you go to the other side and walk clockwise, you'll eventually hit a wall of gravel and stone that is not present going the other way through the tunnel. It's so unstable that digging it away seems like a sure way to destabilize the entire area and possibly destroy the time hole itself; in short, there's a latest date, and it's the one that happened across the passage first.
In fact, this is not a purely time-travel related phenomenon. Rather, it's more like a series of parallel worlds, each with an internal date ten years earlier than the last, all linked by a series of portals in a French cave. If some outside force created the portals, it very likely happened at the "same time" across all of these worlds. Changes to a past world do not propagate to any later worlds, but they do persist in the world that the change was made in. If you go back to 1982 and chop down a tree, then wait six years, 1988 will have a chopped-down tree, but 1998, 2008, and 1018 will NOT have a chopped down tree.
It takes about two hours for an experienced caver to make the loop, meaning that with the eight hours of solid travel one would reasonably expect to achieve in a cave, one could move 40 years into the past. Geologically speaking, the cave extends backwards in time at least a million years in something much like its current state. It's probably still passable for ten or twenty million years back, although traveling far enough to reach that point would take 6,800 years of travel time!
Now, remember this is all hypothetical. I haven't even been to France, as far as you know. With that in mind, what would you do if you happened to be one of the first people to find out about the time hole? And what do you think would happen in general?