"Defence-in-depth" was the theory put forward by Edward Luttwak in his The Grand Strategy of the Roman Empire (1976). The basic idea he endorsed was that the Roman empire, in the later Imperial period, shifted its strategic posture away from "preclusive defence,"which centered on actively addressing external threats while they were still beyond Roman territory. Luttwak proposed that, in the 4th century CE, the Romans began to shift their strategy towards external threats in such a way as to engage them on Roman soil--that is, to fight within the limes rather than outside them.

Luttwak was/is largely viewed as an outsider in the Ivory Tower of Ancient Historians, but his thesis certainly triggered a sort of Renaissance of scholarship on the Imperial army, on the nature of Roman borders, and on the validity of the idea of an Imperial "grand strategy" at any point. At the time, I think his theory was perfectly valid, and the topic(s) of his book are still the subject of much debate. These days, however, I think the archaeological evidence alone is enough to strongly refute him.

Two of the most powerful arguments against Luttwak are Mann ("Power, Force, and the Frontiers of the Empire," JRS 69, 1979, pp.175-83) and Isaac (The Limits of Empire: The Roman Army in the East Oxford 1990). Both point out that there is virtually no archaeological evidence to support a shift in Roman fortifications into the hinterland, and instead we find the opposite: concrete evidence of Roman military presence/occupation in positions well forward of the "established" boundaries of the Empire, even in the 4th century CE. Isaac, who focuses mainly on the the East, obviously, further argues that "defence-in-depth" tends to interpret the ancient world from a modern, grand-strategic mindset that was non-existent at the time. He also talks about "the ideas of modern students" a couple of times, which are certainly jabs at Luttwak and Luttwak's credentials (see quote below).

I don't really have a dog in this hunt, so to speak, but I tend to agree specifically with the point of Isaac that too much emphasis is placed on grand strategic initiatives when it comes to the Romans. I might add that we modern historians tend to do this in ALL periods, not just the 4th century. Roman wars were maddeningly ad hoc, and were more often that not driven by the personal ambitions of the magistrates rather than any overarching strategic thinking. Caesar did not go to Gaul with the intention of establishing a defensible border, at the Rhine or the Rhone or anywhere else, and he never says as much. He plainly tells us that he went to Britannia because he had heard that the Gauls received military aid from that region. This is a plainly "preclusive" frame of mind. He also really just wanted to do it, and to be the first Roman to cross the Ocean. As Isaac suggests, it was much the same in the Imperial period. Wars were fought, or not fought, at the whim of the emperor, and if they were fought it was surely more in pursuit of personal glory than any thought to lines on a map. Here is a bit from Isaac which hits a lot of these points in one neat package. He is talking about military offensives by Vespasian and then again by Trajan in the East:

Cumont, it seems, was the first to interpret the Flavian reorganization as a reaction to events in the sixties [CE]. However, this approach has by no means been generally accepted. It is more common to see the Flavian activity in the East as defensive in nature. This is important, for the assumption that Vespasian wanted 'secure boundaries' itself again justifies another assumption, namely that the existing boundaries were not secure enough. Hence a strategy of defence required another offensive under Trajan. In the words of Luttwak:

AnatoJia now had an organized frontier, but with only two legions in Cappadocia and only three in Syria itself, it could not be a safe frontier. If Parthian forces could assemble freely in Armenia they might strike with' greater forces either due west or due south at thtir choosing, and to the south was Syria, a core province of the Empire. Both strategic necessity and personal ambition required war.

Several observations may be made. First, this scenario is wholly imaginary: Persia several times invaded Syria, but never through Armenia. Second, these arguments are not found in any ancient source: they are formulated by modern students and represent a twentieth- century attempt to reconcile what was in fact a policy of expansion with a strategy thought by modern scholars to be defensive. The real reason, according to Dio, was the emperor's longing for glory. Dio does not lend any support to the theory that there was any other reason for the campaign. Finally, and most important, it is assumed as a matter of course that both the Flavians and Trajans wanted to establish secure boundaries and considered Parthia dangerous. The alternative view recognizes that Romans considered expansion desirable if it could be attained at reasonable cost. Vespasian witnessed the failure of Nero's eastern policy. It is perfectly reasonable to assume both that Vespasian wanted to prepare for a successful conquest of Armenia in future and that Trajan thought he could proceed from there. Trajan, after all, reached the Persian Gulf. No Roman ever claimed that this was necessary for the defence of Antioch on the Orontes.

As to your question of a "home guard" or militia: I don't know enough about this topic to answer confidently. We need a late Roman scholar to talk about the comitatus praesentales, but my understanding is that they were too far removed from the borders to be actors in a "defence-in-depth" strategy.

Sources to consider:

The start of it: E. Luttwak, The Grand Strategy of the Roman Empire (Baltimore 1976)

A good synopis of the whole debate: C.R. Whittaker, "Where Are the Frontiers Now?" in D.L. Kennedy (ed.), The Roman Army in the East (Ann Arbor 1996), 25-41.

Aftershocks: D. Cherry, Frontier and Society in Roman North Africa (Oxford 1998).

Mattern, S.P., Rome and the Enemy. Imperial Strategy in the Principate (Berkeley 1999).

Sommer, C.S., "Why there? The positioning of forts along the riverine frontiers of the Roman Empire." in The Army and Frontiers of Rome (ed. W.S. Hanson), JRA Supplemental Series 74, 2009, 103-14.