A crosslink or a trapped cleavage complex is a problem, but it is not yet a double-strand break. The conversion happens when the replication machinery arrives.
During S phase, the replicative helicase unwinds the duplex ahead of the polymerase, and each strand is copied by a dedicated polymerase. An interstrand crosslink is a covalent bridge between the two templates. The helicase cannot melt it, and the polymerase cannot read through it, so the fork stalls. A stalled fork is not automatically fatal — the cell has fork-protection and repair pathways — but if the block is not removed, the fork can collapse. Collapse means the replication apparatus disassembles and the exposed single-stranded template is cleaved, producing a double-strand break at the fork. A single unrepaired interstrand crosslink is sufficient to kill a replicating cell, which is why these agents are so potent.
A topoisomerase cleavage complex produces the same outcome by a subtly different route. The trapped enzyme holds a nick or a double-strand cut with the enzyme still attached. When the replication fork reaches this complex, the advancing fork physically collides with the trapped enzyme. The collision converts the reversible, protein-linked break into an irreversible double-strand break, and it also releases the enzyme from the DNA. This is why topoisomerase poisons are far more toxic to dividing cells: the drug creates a latent lesion, and the fork collision is what detonates it.
The same logic explains the quiescent-cell tolerance. A cell in G0 is not replicating, so its forks never arrive at the lesion. The crosslink or the trapped complex persists, but without a fork collision it does not become a double-strand break. Transcription can also collide with these lesions and cause damage, but the dominant lethal event in proliferating cells is the replication fork collision. This is the phase-specific selectivity logic of this drug class: the drug is present in all cells, but only cells that replicate their DNA convert the lesion into the lethal double-strand break.