Examples of when a bitwise swap() is a bad idea?

You're not supposed to treat object pointers as pointers to raw binary data in OOP languages, including C++. Objects are "more than" their representation.

So, for example, swaping two objects by swapping their bytes is incorrect:

template<class T>
void bad_swap(T &a, T &b)  // Assuming T is the most-derived type of the object
{
    char temp[sizeof(T)];
    memcpy(temp, &a, sizeof(a));
    memcpy(&a, &b, sizeof(b));
    memcpy(&b, temp, sizeof(temp));
}

The only situation, however, in which I can imagine this shortcut causing a problem is when an object contains a pointer to itself, which I have rarely (never?) seen in practice; there may, though, also be other scenarios.

What are some actual (real-world) examples of when a correct swap would break if you performed a bitwise swap?
I can easily come up with contrived examples with self-pointers, but I can't think of any real-world ones.