```python
from typing import List

def hold_queue(callers: List[int], limit: int) -> List[int]:
    if limit <= 0:
        raise ValueError("Limit must be greater than zero.")

    # If limit is 1, only the caller added most recently will stay
    if limit == 1:
        return [callers[-1]]

    # Use a heap to keep track of callers along with their last arrival time
    import heapq
    heap = []
    for i, caller in enumerate(callers):
        # Remove outdated callers first
        while heap and heap[0][1] < i - limit:
            heapq.heappop(heap)
        
        # Add the new caller to the heap
        if heap:
            heapq.heappush(heap, (caller, i))
        else:
            heapq.heappush(heap, (caller, i))

    return [heapq.heappop(heap)[0] for _ in range(len(callers))]
```