In IBM's Qiskit online simulator, we have the (non-reversible) ability to set a specific qubit to $| 0\rangle$. This is convenient but I'm left confused as to what happens to the elements of the statevector. The amplitudes must go somewhere so the probability is conserved, and I imagined at first that the 0 component for each 'Hadamard pair' absorbs the missing amplitude. But this does not take the phase into account.
What happens in the simulator when we set a qubit to $|0\rangle$?