What does String do that I'm not doing? c++11

I am still new to c++, so bear with me.

I was trying to learn more about how std::move works and I saw an example where they used std::move to move the string to a different function and then showed using std::cout that no string remained. I thought cool, let's see if I can make my own class and do the same:

#include <iostream>
#include <string>

class integer
{
private:
    int *m_i;
public:
    integer(int i=0) : m_i(new int{i})
    {
        std::cout << "Calling Constructor\n";
    }

    ~integer()
    {
        if(m_i != nullptr) {
            std::cout << "Deleting integer\n";
            delete [] m_i;
            m_i = nullptr;
        }
    }

    integer(integer&& i) : m_i(nullptr)  // move constructor
    {
        std::cout << "Move Constructor\n";
        m_i = i.m_i;
        i.m_i = nullptr;
    }
    integer(const integer& i) : m_i(new int[1]) {  // copy constructor
        std::cout << "Copy Constructor\n";
        *m_i = *(i.m_i);
    }
//*
    integer& operator=(integer&& i) {   // move assignment
        std::cout << "Move Assignment\n";
        if(&i != this) {
            delete[] m_i;
            m_i = i.m_i;
            i.m_i = nullptr;
        }
        return *this;
    }
    integer& operator=(const integer &i) {   // copy assignment
        std::cout << "Copy Assignment\n";
        if(&i != this) {
           m_i = new int[1];
           *m_i = *(i.m_i);
        }
       return *this;
    }
    int& operator*() const { return *m_i; }
    int* operator->() const { return m_i; }

    bool empty() const noexcept {
       if(m_i == nullptr) return true;
       return false;
    }

    friend std::ostream& operator<<(std::ostream &out, const integer i) {
       if(i.empty()) {
           std::cout << "During overload, i is empty\n";
           return out;
       }
    out << *(i.m_i);
    return out;
    }
};

void g(integer i) { std::cout << "G-wiz - ";std::cout << "The g value is " <<  i << '\n'; }
void g(std::string s) { std::cout << "The g value is " << s << '\n'; }

int main()
{
    std::string s("Hello");

    std::cout << "Now for string\n";
    g(std::move(s));
    if(s.empty()) std::cout << "s is empty\n";
    g(s);
    std::cout << "\nNow for integer\n";
    integer i = 77;
    if(i.empty()) std::cout << "i is " << i << '\n';
     else std::cout << "i is not empty\n";
    g(i);
    std::cout << "Move it\n";
    g(std::move(i));  // rvalue ref called
    if(i.empty()) std::cout << "i is empty\n";
    g(i);

    return 0;
}

And this is my output:

Now for string
The g value is Hello
s is empty
The g value is

Now for integer
Calling Constructor
i is not empty
Copy Constructor
G-wiz - Copy Constructor
The g value is 77
Deleting integer
Deleting integer
Move it
Move Constructor
G-wiz - Copy Constructor
The g value is 77
Deleting integer
Deleting integer
i is empty
Copy Constructor

Process returned 255 (0xFF)   execution time : 4.284 s
Press any key to continue.

As you can see, it crashes when it enters g the second time, never even getting to the operator<<() function. How is it that the empty std::string s can be passed to g where my empty integer i crashes the program?