Every star shrinks. Depending on the size of a star it will turn into something.
A star can turn into many things. Black Holes, Black Dwarf, White Dwarf, Nuetron Star, Phazar. And much more.
if Our sun was to end today, it would probably turn into a Black Dwarf. The sun is 2 small to turn into anything much. Though I think It will end along with the earth when God says so. And in the book of Rev it says that the sun will turn into a great dark ball.