Since 1573, after the ruling Jagiellon dynasty died out.

Poland was not a traditional hereditary monarchy.

Instead, we had elections where the nobility chose the king from several candidates. That king would serve until his death, and was bound by promises to the nobility and privileges granted to the nobility by his predecessors. His children did not automatically inherit the throne, instead his successor was elected - though it happened that children were elected so they had mini-dynasties.

One of such dynasties was the Saxon dynasty: Poland was in a personal Union with Saxony until 1763 ( same king)

In the 1764 election, a local noble was chosen: Stanislaw August Poniatowski. He was the last king whose reign ended with the partitions of Poland. But, legally, his children did not hold any claim to the throne.

HOWEVER, the 3rd of May Constitution, ratified before the second partition of Poland, stipulated that the Wettin dynasty (rulers of Saxony, as mentioned earlier) would be hereditary rulers of Poland.

The last heir of the Wettin dynasty, Maria Emanuel von Wettin, died childless in 2012. To pass his mantle, he adopted Alexander de Saxe-Gessaphe, Margrave of Meissen as his son (Alexander was actually the oldest son of his second sister). This caused some controversy within the family, and there is a second claimant to be the head of the house, prince Rüdiger,Margrave of Meissen

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SOURCE:

WRITTEN BY Zbigniew Łobocki,

 https://www.quora.com/What-happened-to-the-Polish-Royal-family-after-the-partitions-of-Poland-Are-there-any-descendants-of-them-alive-today