Why would a decrease in the sun's radius cause a change in Earth's orbit? From those to articles it sounds like the mass of the sun will remain about the same, so the orbit should remain about the same. And less mass will cause the orbit to migrate outwards.
Shrinking of the star simply makes it possible to come within the roche limit without being inside the star. The inspiral would happen due to separate processes e.g. friction as the star sheds its envelope or due to interactions between multiple planets.
When the Sun enters the red giant phase, will the radius have expanded enough to consume the earth? I'm trying to remember if that was something my physics professor said years ago or if I heard it from someone less reliable and am merely attributing it to him...
Wikipedia says the sun is expected to expand out to roughly the orbit of Venus (consuming it and Mercury) and turning Earth into a blob of molten rock.