Understanding the definition of endless sets
Defining endless sets, you probably assume that you don't have the Axiom of regularity.

A set is endless when it doesn't contain only simple elements, it has to contain an other set among his elements, and this other set has again to contain an other set and this third set has to contain an other set, etc..

For example, a set verifying $M = \{M\}$ is endless because it contains an other set ($M$) which contains an other set (still $M$) which contains an other set ($M$), etc.. You can take $X=X_0= X_1= ... = M$ as infinite family.

A counter example is $M = \{42\}$; $M$ doesn't contain any set. $M= \{42, \{12\}\}$ is also a counter example because $M$ contains a set ($\{12\}$) but this set doesn't contain any set.