There are two main forces that give a star its size – the atomic fusion that pushes out from the center, and gravity that pulls everything in towards the center. There are also two main parts of a star, the dense inner core (where the fusion happens) and the less dense upper layers
For most of a star’s life, atomic fusion happens at a relatively constant rate, so the size is pretty stable. But when it starts running out of hydrogen, the primary fuel for fusion, gravity starts winning and the core becomes compressed. The compression of the core generates heat (proportionally more than fusion, in which a lot of energy goes into light instead), which causes the upper layers to expand.
So this first stage of death causes it to get larger, but only in terms of diameter – it grows by becoming less dense.
Eventually, the dying core becomes so compressed and hot that the helium (output of hydrogen fusion) can itself undergo fusion, creating carbon. Eventually, the star burns through the helium as well and the now-mostly-carbon core starts to compress under its own gravity.
Here there’s a splitting point.
If a star has enough mass, there can be enough force from gravity to cause the carbon to fuse. There are a couple more cycles of fusion and gravity compression until the core is iron. Iron is a kind of stopping point – for any atom smaller than iron, fusion releases more energy than it consumes, allowing the reaction to be self-sustaining. But fusion of iron (and larger atoms) costs more energy than it releases. Once the core is mostly iron, there is a final gravity compression that becomes so dense that the structure of individual atoms collapses causing a supernova.
If a star doesn’t have enough mass at any of the gravity compression points to trigger the next round of fusion, the core slowly cools down and the upper layers float away and become a nebula
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