Realloc setting pointer to empty

You've forgotten to assign the new value to *s in the function that contains realloc().

void test(void)  // Unaltered; still broken!
{
    char *c = malloc(strlen("I like coffe") + 1);
    strcpy(c, "I like coffe");
    char **s = &c;
    while (strlen(*s) < 25)
        my_function(s);
}

void my_function(char **s)  // Fixed one way
{
    char *w  = *s;   
    size_t len = strlen(w) + 1;  // Define and initialize len

    char *tmp = realloc(w, len + 2);
    if (tmp != NULL)
        w = tmp;
    *s = w;  // Reassign to `*s`
}

Or, more simply:

void my_function(char **s)  // Fixed another way
{
    char *w  = *s;   
    size_t len = strlen(w);  // Define and initialize len

    char *tmp = realloc(w, len + 2);
    if (tmp != NULL)
        *s = tmp;  // Reassign to `*s`
}

Assigning to w only sets the local variable which is a copy of *s; it does not reset the pointer in the calling code.

Note that even with this fix, the loop in test() is going to run a long time because nothing changes the length of the string in c. There's also another problem: you don't pass the address of s to my_function(), so my_function() can't modify s.

void test(void)
{
    char *c = malloc(strlen("I like coffe") + 1);
    strcpy(c, "I like coffe");
    while (strlen(c) < 25)
    {
        my_function(&c);
        strcat(c, "AZ");  // Grow string — not good in real code
        printf("%2zu: <<%s>>\n", strlen(c), c);
    }
}

void my_function(char **s)
{
    char *w = *s;   
    size_t len = strlen(w) + 1;  // Define and initialize len

    char *tmp = realloc(w, len + 2);
    if (tmp != NULL)
        *s = tmp;  // Reassign to `*s`
}

This does away with the pointer to pointer to char in test(). If that's crucial, there's more thinking to be done.

^{Code not formally tested yet!}

Code now tested — can you say "pig's ear"? Copy'n'paste of the wrong material made my test code fail. Here's the instrumented working version — valgrind gives it a clean bill of health.

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

static void my_function(char **s)
{
    char *w = *s;
    size_t len = strlen(w) + 1;  // Define and initialize len
    printf("M1: %p: %2zu: <<%s>>\n", (void *)w, len, w);

    char *tmp = realloc(w, len + 2);
    if (tmp != NULL)
        *s = tmp;  // Reassign to `*s`
    printf("M2: %p: %2zu: <<%s>>\n", (void *)*s, strlen(*s), *s);
}

static void test(void)
{
    char *c = malloc(strlen("I like coffe") + 1);
    if (c == 0)
    {
        fprintf(stderr, "Out of memory\n");
        exit(EXIT_FAILURE);
    }
    strcpy(c, "I like coffe");
    printf("T1: %p: %2zu: <<%s>>\n", (void *)c, strlen(c), c);
    while (strlen(c) < 25)
    {
        my_function(&c);
        printf("T2: %p: %2zu: <<%s>>\n", (void *)c, strlen(c), c);
        if (c == NULL)
        {
            fprintf(stderr, "Out of memory\n");
            exit(EXIT_FAILURE);
        }
        strcat(c, "AZ");  // Grow string — not good in real code
        printf("T3: %p: %2zu: <<%s>>\n", (void *)c, strlen(c), c);
    }
    free(c);
}

int main(void)
{
    test();
    return 0;
}