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It depends somewhat on WHAT you're trying to keep out. If it is something that starts off underground, e.g. moles, then yes, the apron needs to start off underground a ways and angle up.
However that's not the case with chickens. The only thing that you might even POSSIBLY want to keep out that's gonna start out underground is rats, and you know what, you're not likely to be able to keep rats out no matter what
(Certainly not with ANY kind of apron whatsoever, nor buried wire foot-of-fencing either).
So all you really have to worry about here is surface critters, like dogs and skunks and coyotes and so forth. With them, as long as the apron is reasonably wide (2-3' is safest; you would have to go wider for a few individual "very professional" foxes that are out there and have learned to make a living off chicken coops, but most people don't face that situation even if they do have foxes) and the outer edge is not obvious, it works FINE to have it horizontal and at-or-just-below the surface of the ground. And it is, as you can imagine, vastly less work to install it that way
Good luck, have fun,
Pat