To address the CWE-401 (Memory Leak) vulnerability in the given code slice, we need to follow a systematic approach to identify the root cause and then apply an appropriate fix. Here are the detailed reasoning steps:

### Step 1: Root Cause Analysis

1. **Understanding the Code Context:**
   - The function `cancel_channel_subscription` is designed to cancel subscriptions to a channel.
   - It iterates through a linked list of subscriptions (`chan->subscriptions`), checking if each subscription matches the given `sd` (socket descriptor).
   - If a match is found, the subscription is cancelled, and the corresponding list node is freed.

2. **Identifying the Vulnerability:**
   - The code frees the `list` node when a matching subscription is found (`free(list);` at line 16).
   - However, the `list` node contains a pointer to a `subscription` object (`subscr`), which is not freed.
   - This results in a memory leak because the memory allocated for the `subscription` object is not released.

3. **Memory Management:**
   - Proper memory management requires that all dynamically allocated memory is freed when it is no longer needed.
   - In this case, both the `list` node and the `subscription` object it points to must be freed to avoid memory leaks.

### Step 2: Fixing Strategy

1. **Freeing the `subscription` Object:**
   - To fix the memory leak, we need to ensure that the `subscription` object is also freed when a matching subscription is cancelled.
   - This can be done by adding a call to `free(subscr);` after `free(list);`.

2. **Applying the Patch:**
   - The patch involves adding the line `free(subscr);` immediately after `free(list);` to ensure both the list node and the subscription object are freed.

### Conclusion

The patch ensures that both the `list` node and the `subscription` object are properly freed, thus preventing the memory leak. Here is the patched code with the added line:

```diff
<             free(list);
<             if (prev)
---
>             free(list);
>             free(subscr);
>             if (prev)
```

### Final Patched Code

```c
1 static int cancel_channel_subscription(struct nerd_channel *chan, int sd)
2 {
3     objectlist *list, *next, *prev = NULL;
4     int cancelled = 0;
5     if (!chan)
6     {
7         return -1;
8     }
9     for (list = chan->subscriptions; list; list = next)
10     {
11         struct subscription *subscr = (subscription *)list->object_ptr;
12         next = list->next;
13         if (subscr->sd == sd)
14         {
15             cancelled++;
16             free(list);
17             free(subscr); // Added line to free the subscription object
18             if (prev)
19             {
20                 prev->next = next;
21             }
22             else
23             {
24                 chan->subscriptions = next;
25             }
26             continue;
27         }
28         prev = list;
29     }
30     if (cancelled)
31     {
32         logit(NSLOG_INFO_MESSAGE, TRUE, "nerd: Cancelled %d subscription%s to channel '%s' for %d\n", cancelled, cancelled == 1 ? "" : "s", chan->name, sd);
33     }
34     if (chan->subscriptions == NULL)
35     {
36         nerd_deregister_channel_callbacks(chan);
37     }
38     return 0;
39 }
```

By following these reasoning steps, we ensure that the memory leak is properly addressed, and the code is more robust and secure.