This function

const string& foo(); 

does not return a pointer. It returns a constant reference to an object of type std::string. So its return value may not be assigned to a pointer.

According to the C++ Standard

4.10 Pointer conversions [conv.ptr]

1 A null pointer constant is an integer literal (2.14.2) with value zero or a prvalue of type std::nullptr_t. A null pointer constant can be converted to a pointer type; the result is the null pointer value of that type and is distinguishable from every other value of object pointer or function pointer type. Such a conversion is called a null pointer conversion. Two null pointer values of the same type shall compare equal. The conversion of a null pointer constant to a pointer to cv-qualified type is a single conversion, and not the sequence of a pointer conversion followed by a qualification conversion (4.4). A null pointer constant of integral type can be converted to a prvalue of type std::nullptr_t. [ Note: The resulting prvalue is not a null pointer value. —end note ]

So when you use null pointer constant defined with macro NULL it is assigned to the return pointer of the function that will contain null pointer value of type node *

It is a matter of convention and you should clearly have one in your head and document it (at least in comments).

Sometimes a pointer really should always point to a valid address (see this intSwap example, both arguments should be valid pointers). At other times, it should either be such a valid address, or be NULL. Conceptually the pointer type is then by convention a sum type (between genuine pointer addresses and the special NULL value).

Notice that the C language does not have a type (or a notation) which enforces that some given pointer is always valid and non-null. BTW, with GCC specifically, you can annotate a function with __attribute__ using nonnull to express that a given argument is never null.

A typical example is FILE* pointers in <stdio.h>. The fopen function is documented to be able to return NULL (on failure), or some valid pointer. But the fprintf function is expecting a valid pointer (and passing NULL to it as the first argument is some undefined behavior, often a segmentation fault; and UB is really bad).

Some non-portable programs even use several "special" pointer values (which should not be dereferenced), e.g. (on Linux/x86-64) #define SPECIAL_SLOT (void*)((intptr_t)-1) (which we know that on Linux it is never a valid address). Then we could have the convention that a pointer is a valid pointer to a valid memory zone, or NULL or SPECIAL_SLOT (hence, if seen as an abstract data type, it is a sum type of two distinct invalid pointers NULL and SPECIAL_SLOT and the set of valid addresses). Another example is MAP_FAILURE as result of mmap(2) on Linux.

BTW, when using pointers in C to heap allocated data (indirectly obtained with malloc), you also need conventions about who is in charge of releasing the data (by using free, often thru a supplied function to free a data and all its internal stuff).

Good C programming requires many explicit conventions regarding pointers, and it is essential to understand them precisely and document them well. Look for example[s] into GTK. Read also about restrict.

This loop in skipWords is the problem. It'll traverse through the string and beyond because you're not checking for the end of the string.

for(i = 0; wordCount < words; i++)
{
    if(sentence[i] == ' ')
    {
        wordCount++;
    }
}

Since the only way out of the loop is for it to find as many spaces as you've passed in as words, it will always return NULL.

Arguably wordCount should also start at 1 since if there are no spaces in the string, you'll always have at least one word...unless the string is empty.

If the name you are searching for is not at the first element, then you are not searching in the rest of the elements.

You need to do something like -

for (int i = 0; i<names.size(); i++){
    Person* p = names[i];
    if (p->getName() == input) {
        return p;

        // Placing break statement here has no meaning as it won't be executed.
    } 
}

// Flow reaches here if the name is not found in the vector. So, just return NULL
return NULL;

As Chris suggested, try using std::find_if algorithm.

You could return a std::unique_ptr<std::vector<int>> and check that value, or throw an exception, or check vector.size() == 0 etc.