Dying Stars

[Hydraa]

I think you may actually be safe. When a star is created at the beginning it has the chance of having abilities. The abilities and chances a Normal star has is:
1/2 % chance of having 'Star is unstable and could collapse at any time.'
and 1/2% chance of having 'Star is prone to violent eruptions and has an unstable core.'

Both of these are the Star - Unstable ability which is a percent chance of the star exploding. However the normal star with either ability has the ability set to 0 percent.

So if you have not seen the message that the star is exploding you should be safe.

As to the constructed world protecting the star it does do that. A constructed world replaces the star and abilities requiring the star go ahead (cystal tech solar generators even inside the constructed world do not work anymore off that star)