Sure, here's a test case generator for the "Chain-Confined Path" problem statement:

```python
import random

def generate_circle():
    x = random.randint(0, 1000)
    y = random.randint(0, 1000)
    r = random.randint(1, 25)
    return x, y, r

def tcgen():
    datasets = []
    while True:
        n = random.randint(3, 100)
        circles = []
        
        # Generate first circle
        x1, y1, r1 = generate_circle()
        circles.append((x1, y1, r1))
        
        # Generate remaining n-1 circles ensuring they intersect with the previous one
        for _ in range(n - 1):
            while True:
                x, y, r = generate_circle()
                # Ensure this circle intersects with the previous one 
                prev_x, prev_y, prev_r = circles[-1]
                dist = ((x - prev_x)**2 + (y - prev_y)**2)**0.5
                if dist < (r + prev_r) and dist > abs(r - prev_r):
                    circles.append((x, y, r))
                    break
        
        dataset = [n] + circles
        datasets.append(dataset)
        
        # Decide whether to generate more datasets or terminate
        if random.random() < 0.2:
            break
    
    # Format the final input string
    input_str = ""
    for dataset in datasets:
        input_str += f"{dataset[0]}\n"
        for circle in dataset[1:]:
            input_str += f"{circle[0]} {circle[1]} {circle[2]}\n"
    input_str += "0\n"  # End of input
    
    return input_str

# Example usage
print(tcgen())
```

This generator creates random test cases for the "Chain-Confined Path" problem. Each dataset is a list of circles that intersect in a chain-like manner, ensuring the constraints of the problem are met. It also ensures that the circles intersect properly by checking the distances between the centers of consecutive circles.

Feel free to execute the `tcgen` function to generate randomized test cases for your problem!