It's a question of density and tidal forces. The red giant has that mass spread out across a much larger space, so the object that is "straying" has a much more

It's a question of density and tidal forces. The red giant has that mass spread out across a much larger space, so the object that is "straying" has a much more uniform gradient of gravitational attraction across its mass than the white dwarf. An object can only be close to a very small part of the red giant at a time, while an object getting close to a white dwarf is subjected to much more of the gravity well all at once. That makes the gravitational gradient much more pronounced across the object, which means tidal forces are much stronger and more likely to rip the object apart. A good way to think about it is by looking at where the Roche limit exists for a mass of that size. Since the red giant is much larger but has roughly the same mass as the white dwarf, the Roche limit probably exists somewhere behind the surface, while the same orbit would extend far past the surface of the white dwarf. Let's say we have an orbital body around a giant star whose mass dictates that its Roche limit is 0.1AU, and then lets say that the star's diameter is 0.3AU. The object could never get close enough to the star to break apart. Now, that same star collapses while losing a negligible amount of mass, and now is a white dwarf with a diameter of 0.01AU. The object could now approach close enough that it gets pulled apart by tidal forces since its unimpeded by the stars surface all the way down to 0.1AU. https://en.wikipedia.org/wiki/Roche_limit https://en.wikipedia.org/wiki/Roche_limit EDIT: After reading, I realized that I unnecessarily introduced a non-astronomical term in gravitational gradient when I could have just said tidal force. It's the same thing. My apologies to any sticklers out there :)