Here is a working example illustrating the functioning of custom new handlers.
#include <iostream>
#include <new>
/// buffer to be allocated after custom new handler has been installed
char* g_pSafetyBuffer = NULL;
/// exceptional one time release of a global reserve
void my_new_handler()
{
    if (g_pSafetyBuffer) {
        delete [] g_pSafetyBuffer;
        g_pSafetyBuffer = NULL;
        std::cout << "[Free some pre-allocated memory]";
        return;
    }
    std::cout << "[No memory to free, throw bad_alloc]";
    throw std::bad_alloc();
}
/// illustrates how a custom new handler may work
int main()
{
    enum { MEM_CHUNK_SIZE = 1000*1000 }; // adjust according to your system
    std::set_new_handler(my_new_handler);
    g_pSafetyBuffer = new char[801*MEM_CHUNK_SIZE];
    try {
        while (true) {
            std::cout << "Trying another new... ";
            new char[200*MEM_CHUNK_SIZE];
            std::cout << " ...succeeded.\n";
        }
    } catch (const std::bad_alloc& e) {
        std::cout << " ...failed.\n";
    }
    return 0;
}
I do not suggest the demonstrated strategy for production code, it may be too heavy to predict, how many allocations will succeed after your new_handler is called once. I observed some successful allocations on my system (play with the numbers to see what happens on yours). Here's one possible output:
Trying another new...  ...succeeded.
Trying another new...  ...succeeded.
Trying another new...  ...succeeded.
Trying another new...  ...succeeded.
Trying another new...  ...succeeded.
Trying another new... [Free some pre-allocated memory] ...succeeded.
Trying another new...  ...succeeded.
Trying another new...  ...succeeded.
Trying another new...  ...succeeded.
Trying another new... [No memory to free, throw bad_alloc] ...failed.
Process returned 0 (0x0)   execution time : 0.046 s
Press any key to continue.
Instead, from my perspective, do the release of a safety buffer only for terminating your program in a safe way. Even proper exception handling needs memory, if there isn't enough available, abort() is called (as I learned recently).