Did a little more looking when I had time and discovered a bug in com_finder that complicates this issue, but here's how it's (IMO) supposed to work as well as a workaround for the bug.
The word "not" carries a boolean meaning, so when you enter the string
it takes on the meaning I suggested in one of my comments, that of 'every response to an empty query except those containing the word "connected."' Since the result of an empty query is an empty set, you end up with nothing found.
To "unload" the boolean meaning, we surround it with quotes, like this:
While that is the theory behind it and how it's supposed to work, unfortunately, that query triggers the bug I referred to, so instead of interpreting that query as searching for the word "not" and the word "connected" it searches for the word "not" and then resurrects the boolean meaning we were supposed to be eluding and excludes all entries that have "connected" in them from the returned result set. Subtle bug, eh?
So, how do we work around this? So long as there's only one boolean term in your search, put it in quotes and make it the last term:
and that will get you the results you're looking for, all entries with both "not" and "connected" in them.