Certainly! Here is a test case generator for the given problem statement "D: Rescue a Postal Worker":

```python
import random

def generate_graph(n, m):
    edges = set()
    while len(edges) < m:
        x = random.randint(1, n)
        y = random.randint(1, n)
        if x != y:
            w = random.randint(1, 1000)
            edge = (x, y, w) if x < y else (y, x, w)
            edges.add(edge)
    return list(edges)

def tcgen():
    # Number of vertices in the graph (n)
    n = random.randint(3, 1000)
    # Number of edges in the graph (m)
    m = random.randint(1, 2000)
    # Number of dropped mail (k)
    k = random.randint(1, 6)
    # Starting vertex (p)
    p = random.randint(1, n)
    
    # Generate the edges of the graph
    edges = generate_graph(n, m)
    
    # Generate the dropped mail and their destinations
    mails = []
    mail_vertices = set()
    for _ in range(k):
        s = random.randint(1, n)
        t = random.randint(1, n)
        while s == p or t == p or s in mail_vertices:
            s = random.randint(1, n)
            t = random.randint(1, n)
        mail_vertices.add(s)
        mails.append((s, t))
    
    test_case = f"{n} {m} {k} {p}\n"
    for x, y, w in edges:
        test_case += f"{x} {y} {w}\n"
    for s, t in mails:
        test_case += f"{s} {t}\n"
    
    return test_case

# Example usage:
if __name__ == "__main__":
    print(tcgen())
```

### Explanation:

1. **Graph Generation:**
   - `generate_graph`: A helper function to generate unique edges in the graph. It ensures that no self-loops or duplicate edges exist.
   - We ensure the edges are unique by using a set and only adding the edge if it doesn't already exist in the set.

2. **Main Function (`tcgen`):**
   - Randomly selects the number of vertices (`n`), edges (`m`), dropped mail (`k`), and the starting vertex (`p`).
   - Calls `generate_graph` to get a list of edges.
   - Generates dropped mail locations and their destinations ensuring they are not at the starting vertex and there are no duplicates in the mail vertices.
   - Constructs the test case string in the required format.

3. **Output:**
   - The test case is returned as a formatted string ready to be used for input in the problem.

You can run this script to generate random test cases that adhere to the problem's constraints.