In terms of answering this question, it is important to set out the relevant terminology, so I will discuss two different definitions for which thegn could be used in the sources.

The word thegn only really became dominant in the sources from the 10th century, and it is of value to trace its origin back into the earliest Anglo-Saxon literary sources. In the earliest Kentish lawcodes, from about A.D. 600-650, secular nobles were referred to as eorls or eorlcund. Between A.D. 650-700, the above terms were largely replaced in the law codes with Gesith and Gesithcund. In the early-to-mid eighth century, Gesith emerged as the common term for the noble in two senses. In the first sense, it was the title for the estate holder; the warrior who had been rewarded for his service with a land grant. In the second sense, it was the common term for the experienced retainer. In the poem Beowulf, a regular distinction was drawn between the duguð and the geoguð in terms of experience and service within the retinue. This hierarchy of retainers will become relevant at a later point in this discussion. I have drawn attention to these different terms in the hope that I will avoid confusion when I use terms other than thegn.

So going back to Ine’s lawcodes, which are thought to have been written in the late-seventh century, there is a clause about how if a gesithcund holding land neglects the fyrd (which was essentially at this point a primitive shire-based system of military service), then he should pay a fine and forfeit his land. This is one kind of thegn (using one of the gesith definitions from the early-eighth century). Now interestingly, this type of military service, as a condition of land tenure, was a product of bokland, an area of land granted by charter. Under traditional landholding, this kind of stipulation would have been unnecessary, as a holder of land within the king’s territory was by definition culturally obliged to serve the king, but with the emergence of Bokland after Augustine’s mission, the common burdens needed to be imposed to maintain this service between generations, as obligations were personal rather than inherently tied to land.

This type of military service was intermittent, typically short-lived, and defensive. When the campaign ended, they simply returned to their land. There is no reason to think that anything different would happen upon the death of their regional lord or their king. Rather, they would likely then swear fealty, or negotiate overlordship with the victorious party. The nature in which this would occur would depend significantly on the period. Really from the sixth to the late-eighth or even ninth century, when kingship was predominantly itinerant, this would probably involve incorporation into the circuit of the victorious king (or perhaps some of his retainers), essentially a form of surplus extraction. In later periods, when the cash economy was more established and kingship was more centralised on royal centres, this may have involved extraction of cash or easily transportable luxury goods.

However, this still leaves a question about the second type of thegn, the duguð of Beowulf, at which point it may be briefly useful to consider the institution of a retinue. Because Anglo-Saxon England was such a malleable period, it is difficult to universalise, as there were significant regional and temporal differences. To get an idea of retinue culture, it may be useful to read some of the period’s war-poetry, such as Beowulf or Y Gododdin. The homoeroticism often apparent within such poetry demonstrates the close personal (and probably, at times, sexual) bond which existed between the men of the retinue. The reason I mention this is because personal loyalty and personal honour, and the status it brought, were fundamentals within this kind of arrangement. Therefore, when battle took place, the king would be surrounded by the most trusted retainers in his retinue. It is a logical inference that if the king was killed, then his closest retainers would be unlikely to survive. This was apparently the case at the Battle of Nechtasmere, as it is reported in the primary sources that King Ecgfrith was cut down alongside his bodyguards, though of course we have to ask the usual questions about trusting the sources at face value. Given the social importance of honour and hierarchies, it is hard to imagine that, on the battlefield, kings would often die before their retainers. This impression is further reinforced by the entry for 755 from the Anglo-Saxon Chronicle. Simply reading the entry would be far better than reading me summarising it, but essentially two bands of men were butchered because they would not yield due to their loyalty to their king.

However, I’m sure there were instances when thegns survived. Although I can’t think of anything directly relevant in the sources for these instances, I see two (or three) logical paths for which they would follow. First, would simply be retirement. The idea that anyone would have served in a king’s retinue for several decades is more popular than realistic. Even the most veteran of commanders would eventually “retire” if they were able to avoid death up to that point. Most of the king’s close retainers would already have been rewarded with sufficient land to retire comfortably on the death of the king, if they were able to survive the onslaught responsible for the king's death. Those who did not yet have sufficient land or resources would presumably not have been in service long enough to establish the close personal bonds of the comitatus. Therefore, it is possible that they would either have entered the service of a separate, perhaps even a rival king. Otherwise, they may have entered the retinue of the king’s successor. Unfortunately, much of this last paragraph has been speculation, but that is often the nature of this period. There is little which we can say confidently, but I can confidently say that when kings were killed in battle, many of their retainers, particularly their closest and most loyal ones, would not have survived. Those who did may have taken different paths, but a lavish retirement was certainly not unlikely, as military service was deeply rewarding - the gift-giving culture on display in Beowulf illustrates this well.

I know this isn’t the perfect answer, but hopefully it satisfied at least some of your curiosity on the topic.