In Westminster parliamentary systems, ministers must be a member of parliament. They can be from the upper house as well, and so are not necessarily elected in any sense of the word.
In many other countries however that's illegal - being an MP and a minister are incompatible mandates. The Netherlands is one such country; ministers are often drawn from the ranks of parliament (they'll have to waiver their seats in order to take office) but it's not uncommon for a political outsider to be awarded a post. It's accurate to say that we don't elect our executive branch, we merely influence what it will look like by the composition of parliament.
I don't know Italy's constitutional structe in any detail, but presumably they don't require their ministers to be members of parliament. Monti's technocratic government is endorsed by the majority in parliament, and will stay put only until the next elections or until they're sacked by a vote of non-confidence. Therefore, no problems as far as democracy is concerned.
This concludes today's lesson in constitutional theory.
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