The houses follow the male lines. If a British prince marries a Spanish princess then it is still the British royal family and not the Spanish. So when they become King and Queen and then die without any living spawn the Spanish King and brother of the late British Queen would still not carry the British royal house on even though they are closely related. More then likely they have to go back a few generations to find a British prince who did not become a King but rather got a Duchy or something in Germany and started their own dynasty.
It depends on the “laws” or traditions of primogeniture of that particular country/state/tribe. And it can also be political. I suggest you might be thinking of noble inheritances.
They don’t literally die out but if it happens that the tradition indicates that the next in line has to be from someone from a distant line, then that “line of inheritance” is figuratively dead. For example if the rules are that only living male sons inherit etc and the current generation who have no sons might have to go back a few generations to identify the inheritor. In the case of rather complex intermarriages and multiple inheritances, there may be challenges to who is legitimate etc.
When someone says a royal dynasty “died out”, they are usually talking about the direct patrilineal line only. There are probably or definitely still the numerous descendants of daughters around, but these are usually considered parts of other dynasties.
Take England for an example. The Plantagenets are often considered a different dynasty from the House of Normandy, but they are nonetheless related: the first Plantagenet king, Henry II, was the son of Empress Mathilde, the only surviving legitimate child of Henry I of England, the last king from the House of Normandy.
You also see this in Scotland. After the death of Alexander III in 1286, the only possible candidates for the next monarch were related through daughters of the House of Dunkeld. The first choice was Margaret, Maid of Norway, Alexander’s maternal granddaughter. However, she died en route to Scotland from illness and the next two most prominent candidates were John Balliol and Robert de Brus, both of whom were descendants of daughters of the Scottish prince, David, Earl of Huntingdon. Ultimately, Robert de Brus’ namesake grandson won, but his only son David died childless and the Scottish crown passed to Robert II of Scotland, who was the son of David’s half-sister, Marjorie Bruce. Because Robert II’s father was Walter Stewart, he is considered the first of the Stewart kings of Scotland. The Stewarts later became kings of England as well because Henry VIII’s three children died childless, but his older sister, Margaret Tudor, had married James IV of Scotland.
Sometimes, descendants of younger sons are also considered part of a different house, such as in France. Charles IV of France is dubbed the last Direct Capetian king, because he and his brothers all failed to have any surviving sons. While Charles had a daughter, nieces, and a younger sister, his sister had married the king of England and his daughter and nieces were children and most of the French nobility weren’t overly thrilled with any those candidates and bestowed the crown instead instead on Charles’ cousin, Philippe VI. Philippe is considered the first French king of the House of Valois, because his father was Charles, count of Valois, the second surviving son of Philippe III of France. The male-line of the House of Valois died out in 1589 with the death of the childless Henri III of France and the crown passed to the Bourbon Henri IV. Henri IV’s claim to the crown came from the fact that he was a direct descendant of Robert, count to Clermont, one of the younger sons of Louis IX of France. However, his paternal and maternal grandmothers, Françoise d’Alençon and Marguerite d’Angoulême, were both daughters of the House of Valois, which made him more closely related to the Valois kings than his strictly patrilineal descent would have otherwise indicted.
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