I have a sapient species in my setting called "mole-bears". I based their social system on eusocial species, specifically naked mole-rats.
Mole-bears are on average around 100 pounds and look like six-limbed furless, grey wombats with bioluminiscent markings, they live in underground tunnels and cave systems. Queens are significantly larger, sometimes weighing more than 3 times as much as the non-reproducing workers. Mole-rat colonies range from 100 to 300 individuals.
In a mole-bear colony only the queen and her mates reproduce, the rest are sterile female and non-sterile male workers. When the queen dies, another female will take her place, which could theoretically become any female. After the queen dies the females will fight for the position of queen, and the winner goes through some kind of hormonal change that will allow them to reproduce.
However, since everyone in a colony is related I want to know how they would avoid inbreeding, since genetic diversity is generally important for a species.