Hi joe,
The behavior for search in CRM is like this only, you can search only active contacts.
If you try to search an inactive contact with name somehow matching (first 3 or last 3 characters etc) to active contacts, the search result will display only active contacts. They have provided a search box for inactive records but it doesn't work, actually there is no provision for it.
You are not demanding too much; you might get a solution in upcoming roll-ups.