= Solution
The sequence $\boxed{\ldots000010000.00000\ldots}$ has exactly one $1$ and otherwise zero entries. Under forward shifts that exceptional symbol moves out of every fixed observation window; the same happens under backward shifts in the other direction. Thus both temporal limits are the all-zero fixed sequence, while the orbit itself is nonconstant: it is homoclinic to that <fixed point>. The bi-infinite coding specifies a chosen full orbit even when the original interval map is not invertible.
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