This question is partly inspired by this question.
Abolishing monarchies is traditionally done via a revolution (I'm not aware of any instances of the converse). If the revolutions turn out violent, like in France and Russia, the royals and possibly other nobles tend to get executed. However, there are also cases, notably Serbia, where a viable descendant is available. So, basically, once a monarchy is abolished, there are two options: there either are (direct or otherwise) descendants of the royal family and/or other noble families left or there aren't.
Have there been instances of a monarchy being reintroduced in a country in either of those cases?
I imagine that it would be somewhat harder to just "reinvent" some royal family than to reinstate an already living one. There is also the possibility of elected monarchs, but I think that is just theoretical. In any case, there must be political incentive to do so, in the case of a republic, some party must somehow push trough the required constitutional and other changes. The required support would presumably imply that they are also the ruling party and probably that he current head of state is a dominant member of that party, so basically they would undermine their own power, which is a hard thing for politicians to do.