Sure! To write a test case generator for this problem, we'll follow these steps:
1. Generate a random length for the string \( S \) within the given constraints.
2. Generate a random string \( S \) consisting of characters 'a', 'b', and 'c'.
3. Return the generated string.

Here's the Python code to do this:

```python
import random

def tcgen():
    # Generate a random length for the string S
    length = random.randint(2, 2 * 10**5)
    
    # Generate a random string S consisting of characters 'a', 'b', and 'c'
    S = ''.join(random.choice('abc') for _ in range(length))
    
    return S

# Example usage to generate a test case
if __name__ == "__main__":
    test_string = tcgen()
    print(test_string)
```

This code will generate a random test case that meets the constraints of the problem statement. The length of the string \( S \) will be between 2 and 200,000, and the string itself will be composed of the characters 'a', 'b', and 'c'.