How could the fabric of spacetime rip apart?
The “Big Rip” idea is speculative: it could involve matter in gravitationally bound systems (currently unaffected by the cosmic acceleration) getting pulled apart, and perhaps even later having electromagnetically and strongly bound systems (atoms, nuclei) ripped apart, and then maybe even having “spacetime itself” ripped apart. It’s not clear what the latter means, since a good theory of spacetime on a quantum scale has not yet been developed. But another possibility is that everything just gets very far apart and dark and cold and lonely. We need some better ideas about what’s causing the acceleration before we can really evaluate these possibilities.