The saving is arithmetic rather than invention. Treasury and the IRS, summarizing comments in the preamble to a digital-asset broker reporting rule, recorded the mechanism directly: "some distributed ledgers enable transactions to be aggregated on a layer 2 blockchain before being recorded as a single transaction on the primary distributed ledger." The base chain charges for the work it does, so recording one transaction instead of five hundred spreads a single base-chain cost across all of them. That is the whole economic argument. The layer 2 also charges for its own work, so the cost is reduced rather than removed, and the mechanics of what a base-chain fee is and how it is set belong with gas fees rather than here.
What a layer 2 inherits, and what it does not. The feature that distinguishes this arrangement from an exchange keeping a private internal tally is that the layer 2 records its results to the base chain, so the outcome is meant to be checkable against a public ledger rather than only against one company's books. What it does not inherit is the base chain's software, its operators or its history. While a balance sits on the layer 2, its correctness and its availability depend on the layer 2's own code and on whoever runs that network, in addition to the base chain underneath. A crypto token is already an exposure to two things at once, the token itself and the network it needs in order to exist and to move. Held on a layer 2 it becomes three: the token, the layer 2, and the base chain the layer 2 settles to.
Where the asset actually is, which is the practical point for a household. Because the layer 2 keeps its own record, moving an asset onto one is a change of location and not merely a change of speed. The balance is recorded on that network, so a block explorer or a wallet view pointed at the base chain alone will not report it, and a holder has to know which network a given balance is on in order to find it, move it or account for it. That is also why an exchange or a custodian may support an asset on the base chain and not on a particular layer 2, or the reverse. The question to ask about any crypto balance is which network it is on, not merely which asset it is.
Crossing between the two networks is done by software, and the usual limits on that software apply. Transfers in and out depend on program code running on each side, and the CFTC's own primer attaches a standing caution to code of that kind: a smart contract "is not necessarily 'smart'" and "may not be a legally binding contract." Nothing about a network being called a layer 2 changes what that code can and cannot guarantee.
The label has already been argued over in a rulemaking without ever acquiring a definition. In the comment round on the Treasury and IRS digital-asset broker reporting rule, one comment urged that persons who record transactions on these secondary networks "using sequencer software" be treated the way validators are treated for the purposes of the broker definition. Congress later disapproved that rule under the Congressional Review Act, so none of it is live law. The argument still shows what is at stake in the label: a question about who is doing the recording, and therefore who reports. Every tax question that follows from holding or moving an asset on one of these networks belongs with crypto taxes, including the basis and disposal questions a transfer raises.