The Sun, our star, will eventually __ and become a __.'

The sun, our star, will eventually die and become a white dwarf.

Explanation:

When a star dies it goes through a process in which it is called "The lifecycle of a star."

If the sun were to go theough this process and die out, it would eventually reach to the point it can either be a white or black dwarf, but there is more of a possibillity of it becoming a white dwarf than a black dwarf.