Some notable examples coming to mind would be the royal house of Orléans in France (the sole sovereign being King Louis-Philippe, deposed in 1848 after a reign of just 18 years), the royal house of Wittelsbach in Greece (King Otto got deposed in 1862 after a reign of 30 years), the princely house of Wied in Albania (Prince Wilhelm officially reigned from 1914 to 1925, but actively served as sovereign only briefly in 1914 before going into exile), and the princely house of Battenberg in Bulgaria (Prince Alexander reigned for just seven years, 1879-1886, before getting deposed).
The princely house of Hohenzollern-Sigmaringen in Romania could also have qualified as an example of this, since Prince (later King) Carol I and his consort (born Princess Elisabeth of Wied) were unable to produce a surviving child. As it was, the dynasty was saved by the king being able to designate as heir a nephew through his older brother.
Fürst Leopold of Hohenzollern-Sigmaringen (who renounced his own succession rights to the new principality of Romania) had three sons by his wife, born Infanta Maria of Portugal. The eldest (Wilhelm) was to assume the position of heir to his uncle -- only to decide that he didn't want the throne, either. So he renounced his succession rights in favor of his next brother.
Had Prince Ferdinand also decided that he didn't want to become king of Romania, however, it's likely that the house would have been deposed after just a single reign -- notwithstanding the fact that he had a younger brother (Karl Anton). A dynasty can survive only so long, when a succession of eligible heirs renounce their rights to the throne.
Indeed, the house of Wittelsbach might actually have been saved in Greece, had a prince of Bavaria been willing to step up and assume the position of heir to the childless King Otto (who had married Duchess Amalie of Oldenburg in 1836). The constitution of 1843 had made provisions for the succession of the king's younger brothers and their male issue, in the event that Otto failed to produce any heirs of his own. The throne of Greece was basically theirs for the asking, but nobody else in the family seemed terribly eager to take it.
Besides, as everybody knows only too well, the said younger brothers and nephews of King Otto of Greece were also brothers and nephews of King Maximilian II of Bavaria. So these male Wittelsbachs found themselves in the awkward and difficult position of potentially being dual dynasts, since they obviously were also heirs to the Bavarian throne. Aside from Prince Ferdinand (who left Germany and permanently settled in Spain), nobody was going to renounce his succession rights to the German kingdom -- even when the house was still reigning over the Greek.
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