Male line descent from previous emperors, or any descent from previous emperors, was not legally necessary to become emperor. There were Emperors who seized the throne, and officials who were elected emperor when there was no obvious heir to the throne.
Almost every single Emperor after Alexios I Komnenos (reigned 1081-1118) was descended from him either in the male line, like the Emperors at Trebizond, or else through female lines of descent.
The Komneni of Trebizond became extinct in the male line, but the Safavid Dynasty of Persia was descended from them through females, and there are many families descended from the Safavids through female lines.
Almost every emperor after 1204 (except for the rulers of Trebizond and a few others) was descended from Constantine Angelos who married Theodora Komnene, a daughter of Emperor Alexios I, in either male or female lines of descent.
There are no known descendants of the Palaiologos Dynasty in legitimate male lines. There are many families who use the name Palaiologos who may be descended from relatives of Michael VIII, the first Palaiologos emperor, or from illegitimate sons of emperors, or descended from emperors through female lines, or descended from unrelated families which simply took the high prestige name of Palaiologos. Due to loss of records there is no Palaiologos family with any known connection to the dynasty.
Michael VII, the first Palaiologos emperor, had no descent from previous emperors except his father's mother's mother's father was a son of Emperor John II Komnenos and his mother's mother's father was Emperor Alexios III Angelos. If he could become emperor due to descent through female lines, someone can become the rightful heir of the Palaiologos dynasty through female line descent.
Despot Thomas Palaiologos (1409-1465) was recognized in western Europe as the rightful emperor after the fall of Constantinople. His younger son Manuel (1455-1512) returned to Constantinople and had children who became Muslims and their descendants can't be traced.
Andreas Palaiologos (1453-1502), Thomas's older son, also claimed to be the titular emperor but did not have any proven children, legitimate or otherwise. Maria, who married Prince Prince Vasily Mikhailovich of Vereya-Belozersk, may have been a daughter of Andreas.
Zoe/Sophia, daughter of Thomas Palaiologos, famously married Ivan III of Moscow. Her last known descendant, Maria of Staritsa, died in 1610.
Thomas's older daughter Helena married Despot Lazar Brankovic of Serbia. Her daughter Milica Brankovic married Leonardo III Tocco of Epirus and became the ancestor of the Tocco family of southern Italy. The Tocco family became extinct in the male in the 19th century but many of their daughters married into the Neapolitan nobility, so it would be rather simple for experts in the genealogy of the Neapolitan nobility to find the rightful heir of the Tocco family and thus of the Palaiologos Dynasty.
Of course there were many earlier imperial dynasties who had different heirs than the Palaiologos dynasty.