will the sun actually swallow earth as it dies?

That sounds likely
Because as it runs out of Hydrogen it will swell to become a whispy red Giant
Red hot, it will sear earth as well as Venus and Mercury
Mars just might Survive and the Gas Giants will probably be left as Dense Cores
The Sun will finally be left as a White Dwarf
None of it very condusive for life
So hopefully we will have moved by then

Not exactly. As it uses up what remains of its fuel, the Sun will swell into a red giant which MAY be bigger than the Earth's orbit so the Earth MAY end up inside it. Nobody knows exactly how big it will get, except that it will be about that size. Either way, the Earth will certainly be incinerated and be left as a dead ball of rock as the Sun shrinks again and becomes a white dwarf.

The Sun does not have enough mass to explode as a supernova. Instead it will exit the main sequence in approximately 5 billion years and start to turn into a red giant. As a red giant, the Sun will grow so large that it will engulf Mercury, Venus, and probably Earth.

YES!!!
When all the hydrogen and helium in the sun are used up, it will form a 'Red Giant'.
It will be so big that all the inner rocky planets ( Mercury, Venus, Earth & Mars), will be swallowed up.

Yes it will. But fear not! We'll be burned to a crisp long before then.

It may.

Whether it actually does depends not only on how big that the Sun gets, but on what happens to Earth's orbit.

Not die, Expand into a RED GIANT, and yes it will.
4.5 Billion years from now. So we have better find a new place to live by then.

no, the sun will explode

It's not certain, but it probably will...
The sun's outer layers will expand, past the orbit of Mercury, past the orbit of Venus, and possibly enveloping the Earth. The added friction to our planet's motion will slow our orbit - so, we'll begin to spiral inward, and in a few thousand to a few tens of thousands of years, we'll be close enough to the core of the sun that tidal forces will cause the Earth to be pulled apart, and the mass will 'rain' down on the sun's core...

End of cycle, not "dies" .. However hydrogen into helium fusion will stop.

At some point in the distant future the sun's internal gravitation will no longer be able to contain the pressure of fusion and it will expand in to a larger red sun.

As the fusion process runs out of hydrogen l it will shrink increase in temperature and fuse 3 helium atoms into carbon, that done, cool into a dense carbon cinder.

Most of the answers are correct but not complete. The sun will certainly expand into a red giant in about five billion years. But life on earth will be long dead by then. As the sun's output gradually increases over time, the earth will gradually warm up, and some time around 800 million to a billion years from now earth's surface temperature will be too high for liquid water to exist, ending all life.

Most theories I see tell of an expanding/dying sun which expands out to almost the Earth orbit.. giving Mars a probable place to be.

Perhaps.

Not if I swallow it first