Tiger sharks do tend to sink in open water if they stop swimming because they are slightly negatively buoyant. But the broad wording leaves out crucial context: they can still stop swimming, keep breathing, and rest motionless on the seafloor. That omission changes the practical takeaway, so the claim is better treated as an oversimplification than a cleanly true statement.
Caveats
This confuses buoyancy with breathing: tiger sharks can stop swimming without suffocating because they can use buccal pumping.
The statement needs an 'in open water, unsupported' qualifier; near the bottom, a tiger shark can rest rather than continue sinking.
Some popular explainers oversimplify shark biology by treating all sharks as if they must swim constantly.