You are mixing up two uses of "that".
You are entirely correct that if the sentence were:
That one stays; that one glows.
then the plural would be:
Those ones stay; those ones glow.
However, in the actual example sentence (the ones that stay are the ones that glow), "that" is being used as part of a relative clause to provide more information about the antecedent.
The house that she bought was really expensive.
Here, "that she bought" is a relative clause telling you more about the house. It's actually a defining (or restrictive) relative clause, because you aren't just providing more information about the house, you're using the relative clause to specify exactly which house you mean.
In the same way, in your example sentence, "that stay" is specifying exactly which "ones" you mean: the friends (or stars) who stay are the friends (or stars) who glow. You can't replace it with "those" because this is a different meaning of "that" that doesn't have a plural form.
This goes beyond the scope of your question, but if you are interested in further reading about the difference between restrictive and non-restrictive relative clauses, take a look at the usage note at the bottom of The Free Dictionary's page on that. But don't trouble yourself overly over the differences between exactly when you can use "that" and when to use "which" in sentences where they have the same meaning; native speakers are fairly fluid with them in all but the most formal of writing.