```python
"""Prune a file listing with ordered drop and keep rules."""


def prune_listing(listing, rules):
    def segment_fits(pattern, text):
        p = t = mark = 0
        star = -1
        while t < len(text):
            if p < len(pattern) and pattern[p] == "*":
                star = p
                mark = t
                p += 1
            elif p < len(pattern) and pattern[p] == text[t]:
                p += 1
                t += 1
            elif star >= 0:
                p = star + 1
                mark += 1
                t = mark
            else:
                return False
        while p < len(pattern) and pattern[p] == "*":
            p += 1
        return p == len(pattern)

    def split_strict(text, what):
        if not isinstance(text, str) or text == "":
            raise ValueError(f"{what} must be a non-empty string")
        segments = text.split("/")
        if any(segment == "" for segment in segments):
            raise ValueError(f"{what} has an empty segment: {text}")
        return segments

    # Validate every rule and path with split_strict, then keep each
    # path the last matching rule allows; a path no rule matches survives.
    valid_listing = [split_strict(path, "path") for path in listing if isinstance(path, str)]
    valid_rules = [split_strict(rule, "rule") for rule in rules if isinstance(rule, str)]
    if not valid_listing or not valid_rules:
        raise ValueError("All paths and rules must be strings")
    
    result = []
    for path in valid_listing:
        for rule in valid_rules:
            if rule.startswith("!"):
                if not segment_fits(rule[1:], path):
                    break
            else:
                if segment_fits(rule, path):
                    result.append(path)
                    break
        else:
            result.append(path)
    
    return result
```