I think under fares simplification you can't have an Off-Peak fare with no time restrictions because an Off-Peak fare is defined as a fare which has time restrictions
Therefore these fares have to be classified as Anytime
Some TOCs took that view, and there were several 'solutions':-
1) Rename the Saver (SVS/SVR) as Anytime (SOS/SOR).
2) Rename the Saver (SVS/SVR) as Off Peak (SVS/SVR), introduce additional time restrictions, and introduce a new Anytime at an inflated price.
3) Rename the Saver (SVS/SVR) as Super Off Peak (SSS/SSR), introduce additional time restrictions, and introduce a new Off Peak at an inflated price, and a new Anytime (SOS/SOR) at an even more inflated price.
I am aware of flows where the fare from A to B and from A to C that is the former SVR is priced at ~£22. However A to B has this fare re-named SSR, and there are newly created SVR and SOR fares used as fare increases by stealth, while the fare from A to C remains the same price, but is an SOR! So anyone who wants to buy on board and/or travel at peak time from A to B can buy an A to C ticket, and not be 'penalised'.
However, going back to the original point that you can't have an Off Peak ticket that is valid at any time, it's not actually true, and some TOCs have persisted with this, and their SVRs remain identical to the original SVRs except with the Off Peak name. ATW is a good example, say Cardiff to Crewe, there is no SOR for this flow, the only standard class return fare is the SVR, which has an 8A restriction, which is valid at any time, but retains the original SVR restriction of not being valid for break of journey.
So yes, some Off Peak tickets are valid at any time.
There's also an Anytime ticket that purports not to be valid at any time but I believe this is unenforceable as there is documentation on the National Rail website that states that these tickets are valid at any time.