If your application is unable to allocate a physical memory (RAM) block to store information, the operating system takes over and 'pages' or stores sections that are in RAM on disk to free up physical memory so that your program is able to perform the allocation. This is done automatically and is completely invisible to your applications.
So, in your example, on a system that has 1MB RAM free, if your application tries to allocate memory, the operating system will page certain contents of physical memory to disk and free up RAM for your application. Your application will not crash in this case.
This, obviously is much more complicated than that.
There are several ways to configure a page file on Windows (fixed size, variable size and on which disk). If you run out of physical memory, and out of hard drive space (because your page file has grown very large due to excessive 'paging') or reach the limit of your paging file (if it is a static limit) then your applications will fail due out an out-of-memory exception. With today's systems with large local storage however, this is a rare event.
Be sure to read about paging for the full picture. Check out:
http://en.wikipedia.org/wiki/Paging
In certain cases, you will notice that you have sufficient free physical memory. Say 100MB and your program tries to allocate a 10MB block to store a large object but fails. This is caused by physical memory fragmentation. Although the total free memory is 100MB, there is no single contiguous block of 10MB that can be used to store your object. This will result in an exception that needs to be handled in your code. If you allocate large objects in your code you may want to separate the allocation into smaller blocks to facilitate allocation, and then aggregate them back in your code logic. For example, instead of having a single 10m vector, you can declare 10 x 1m vectors in an array and allocate memory for each individual one.