The answer from 2011 is wrong and I don't understand why it was accepted. The question is about the effect of inhomogeneity on a big rip, but the paper cited in the answer assumes perfect homogeneity, so it's irrelevant to the question.
(The paper is also irrelevant to real life, since perfect homogeneity at the atomic level is inconsistent with the existence of atoms. This is a strangely common mistake and I've written several answers about it, including this one. On top of that, even if you do assume perfect homogeneity, the claim in the abstract is still not correct, unless you interpret it tautologically as "systems either expand without bound or don't". Looking at the paper, it appears he only considered some specific functions $a(t)$ for which the conclusion happens to hold. It doesn't hold in general, and it doesn't hold for big rip cosmologies in particular.)
As Luboš Motl said in a comment, there doesn't seem to be any plausible sort of stuff that would lead to a big rip, but if you imagine that something with the necessary properties exists, you can perhaps get an idea of how it might behave in an inhomogeneous world.
In standard cosmology, dark energy is perfectly homogeneous down to subatomic scales. The expansion of the universe is just the relative motion of galaxy clusters, and doesn't push atoms apart, but dark energy does push atoms apart, because it's everywhere. Since it's the same everywhere, it just exerts a small constant outward pressure, so atoms are slightly larger than they would be if $Λ=0$, but don't grow over time.
In slow-roll inflation, the inflaton field is somewhat like dark energy, except it's not constant over time; if it were, there would be no way to coordinate an orderly exit from inflation on a large/infinite spacelike surface. Instead, it has a value that is set by the event that triggers inflation, evolves over time (the slow roll), and triggers the exit when it reaches a certain value. In other words, this all-space-permeating substance has a built-in clock, and in principle you can read the clock by local measurements to determine what phase of inflation you're in.
The quintessence that caused a big rip would be similar to that. Spacetime would be filled with ticking time bombs, and in principle you could read the nearest one's clock face by local experiments. They would be affected by gravity, since everything is. They would be lensed by clumps of matter, and would collide with a result determined by some unknown dynamics. But it's not terribly farfetched to suppose that this wouldn't stop the countdown to doomsday. It just means that the final singularity would not be a nice flat hyperplane, but would have a more complicated shape—as is also the case for a more realistic treatment of the big crunch, taking inhomogeneity into account. In the last few yoctoseconds before the end (according to the nearby clocks), nuclei would be "ripped apart" in the sense that their diameter would go to infinity, though they wouldn't really have time to notice.