It seems extremely unlikely for a monarch not to have a bunch of potential heirs.
Henry, Count of Chambord died in 1883, the last male lineage descendant of King Louis XV (died 1774). The French monarchists were split into two different groups. The Legitimists accepted a distant cousin by male lineage, Juan Count of Montizon, the Carlist claimant to the Spanish throne, as the rightful heir. Their latest common male lineage ancestor had died in 1711, 172 years before. The Orleanists accepted an even more distant cousin as the rightful heir of France. His latest male common ancestor with the Count of Chambord had died in 1643, 240 years earlier.
King Henry IV became king of France in 1589 as the male lineage cousin of king Henry III. Their latest common ancestor in male lineage, King Louis IX, died in 1270, 319 years earlier.
Elector Maximilian II Joseph of Bavaria died without close male relatives in 1777. Bavaria was inherited by his closest male line cousin Charles IV Theodore. Their latest male lineage common ancestor, Duke Louis II of Bavaria, died in 1294, 483 years earlier.
King William III of The Netherlands and Grand Duke of Luxemburg died in 1890. His daughter Wilhelmina became Queen of the Netherlands. But the throne of Luxemburg (which their dynasty hadn't even possessed until 1815) passed by agnatic or male lineage succession. So King William III's closest male lineage relative was the heir. Adolphe, former Duke of Nassau, was the seventeenth cousin once removed of King William III. Their latest common male lineage ancestor, Count Henry II of Nassau, died in 1251, 639 years earlier. Adolphe is considered the most distant relative to ever inherit a throne.
In 1290, the little Queen Margaret, the Maid of Norway, died on her way to Scotland with no close heirs. In the "Great Cause", about fifteen men claimed the Scottish throne. Her closest relative among the competitors, Nicholas de Soules, was her second cousin by an illegitimate line, while the most distant relative, John Comyn, was her sixth cousin once removed.
And when the Lancastrian Prince of Wales and his father King Henry VI were killed in 1471, that was just about the end of the Lancastrian branch of the English royal dynasty. There were no more legitimate descendants of the first Lancastrian King, Henry IV. So there were no possible Lancastrian claimants left, right?
How about King Alfonso V of Portugal (1432-1481) whose grandfather King John I married Philippa of Lancaster, the oldest sister of King Henry IV? King Alfonso's sister's son as the later Emperor Maximilian I, who married Mary the heiress of Burgundy whose grandmother was a daughter of John I and Philippa, thus giving their son King Philip I of Spain a double dose of the Portuguese Lancastrian descent. Philip married Queen Juana la Loca of Spain who was a great great granddaughter of John I and Philippa, adding more to the Lancastrian heritage of his children including Emperors Charles V and Ferdinand I.
Perkin Warbeck, Yorkist claimant to the English throne, agreed that his rights would go to Maximilian if he died without heirs. These facts may partially explain why Maximilian claimed to be the heir to England.
King Henry IV's next oldest sister Elizabeth married the first Duke of Exeter and in 1471 her heir was Henry Holland, 3rd Duke of Exeter (1440-1475).
Henry IV's third sister Catharine married King Henry III of Castile and in 1471 her heir was her grandson King Henry IV, though eventually it would be her granddaughter Queen Isabella I , mother of Queen Juana la Loca. So yet another Lancastrian descent for Emperor Charles V, who some people said had a better claim to the English throne than King Henry VIII. In fact Emperor Charles V did once threaten to invade and conquer England.
As you may remember the Yorkist claim made by descendants of the fifth oldest son of King Edward III was descent through female links from the third oldest son of Edward III, but the Lancastrian claim was through descent from the fourth oldest son of King Edward III, claiming that female descent was irrelevant for inheriting the throne. When Prince Edward and King Henry VI were killed in 1471 their killer Edward IV the Yorkist king thus became their heir according to the Lancastrian claim of seniority by male lineage descent.
So any die hard Lancastrians would have to scramble to find some other claimants. King Henry Iv did have some younger half brothers, the Beauforts, illegitimate children of John of Gaunt, Duke of Lancaster, and Catharine Swynford. John and Catharine were later married in 1396 and their children were legitimated - though it is controversial whether that was valid for succession to the throne.
Unfortunately for Lancastrian supporters, the last two male Beauforts were killed in 1471, leaving only descendants through female lines - and denying the inheritance of the throne though female lines was a main basis of the Lancastrian claim. The senior female heiress of the Beauforts was Margaret Beaufort, mother of King Henry VII Tudor. But Charles Somerset, first Earl of Worcester (c.1460-1526) was an illegitimate and legitimated son of Henry Beaufort, 3rd Duke of Somerset. If any claim to the male lineage inheritance of the throne could pass through an illegitimate but legitimated son, it might better pass through another illegitimate but legitimated son than through a woman of legitimate birth.
And then there were the actual descendants of the House of Lancaster instead of relatives of it. Thomas of Lancaster, Duke of Clarence, had an illegitimate son Sir John Clarence who was allegedly the ancestor of the de Langlee family in France. John of Lancaster, Duke of Bedford, had an illegitimate daughter and a grandson. Humphrey of Lancaster, Duke of Gloucester, had an illegitimate daughter, Antigone of Gloucester, who married the Earl of Tankarville. Their grandson John Grey (died 1497) Baron Grey of Powis was their heir in 1471.
The succession to Queen Elizabeth I of England was widely speculated about during her long reign despite her discouragement of it. Among the many candidates suggested were four claimants to the throne of Portugal and thus to the Lancastrian succession.