I think the question is intended to be, "How does the owner presently receive farm subsidies if the land isn't registered and we don't know who owns it?"

They - or more likely a front company - claims the subsidies. If a form goes in and the claim looks plausible, subsidies are paid. I strongly suspect title isn't checked.

Interestingly, the UK has a "squatter's rights" law not many people know about. If you fence off some land and use it, it effectively becomes your property after a number of years if no one challenges you.

I've seen people use this to extend their gardens into common land.

12 years (or at least it was in the early 90s): we let a neighbouring farmer graze his sheep on some land we had, but had to ceremoniously turf them out every so often to reset any possible claim in law.

Note that legally speaking you didn't actually need to do that -- if they're there with your consent, it's not adverse possession.

That’s a part of the common law where it’s called adverse possession. In the US flavor of common law at least one can never adverse possess land owned by the government.

The subsidy recipient is not necessarily the owner e.g. following mutual agreement a farmer could graze their sheep on the neighbour's land which they don't own (because friendliness or usefulness or family history or specific allowances when the land was sold a hundred years back), and that land could be unregistered.

I expect the idea here is that the subsidy seeker probably has an idea as to whose land it is they're using, and thus could go ping the owner for registration so they can get their subsidies back. This is especially likely if the registration is easy and free: chances are the owner simply has not bothered registering the land because they have no need to and can't be arsed, being asked to by an acquaintance would be sufficient a motivation to eventually check in with the local authorities.