How to make a measurement in a subspace?

I am currently reading this paper by Xin et al. (2020) in which they perform a measurement in a particular subspace. In the caption of Figure 6 (last sentence) they say " At the end of the circuit, we measure the state of the work system in the subspace where all ancilla registers are $|0⟩|0⟩_k |0⟩_{kL}$." What I am having trouble understanding is how they ensure that the ancilla qubits are in the state $|0>$. How do I design my circuit to transform them into this state?