While I can only speak on this in regards to the Romans, it was rather commonplace for them to execute, or send into slavery, enemy soldiers that they captured. I am also not an expert on Roman slavery, but I will try to explain it briefly to the best of my abilities. Ancient Slavery was not like the chattel slavery that was practiced in the United States, and elsewhere, in more modern times. While all slavery, is of course terrible, Roman slavery was not quite as brutal in comparison with its modern counterpart. Salves in the Roman world were usually treated better than African slaves were treated in the 17th-19th centuries (though it should be noted that it was still perfectly legal to beat, or even execute, your own slaves). Roman slaves could run businesses for their masters, and had more "freedom" than the term slave implies. Many slaves could even buy their own freedom if they saved up enough money. The children of these freedmen were even given full citizenship, such as the poet Horace, even though the freedmen themselves were not. Some slaves still would have had extremely difficult lives of course, especially those working in the mines (which would have been excessively brutal). That being said many soldiers likely surrendered to the Romans because slavery may have been seen as a better outcome than death, even though most unskilled slaves had very short lifespans due to the brutality of their work. In regards to just fighting to the death, there eventually comes a point that you simply just can't fight anymore no matter how much you might want to.

That being said there were other outcomes to surrendering than execution and enslavement. The Roman Empire would sometimes allow groups of barbarians who had surrendered to settle within the Empire as laeti.

Another quite widespread category from the third century were the laeti: barbarians captured by the Romans and settled on the land rather being, as was usual, butchered out of hand or thrown to the beasts. (Guy Halsall, *Barbarian Migrations and the Roman West 376-568)

This means that there would have been incentive, a relatively attractive incentive, for barbarian soldiers to surrender if they knew they had been beaten. While there probably was not a large degree of difference between the barbarians admitted into the Empire as laeti and outright slaves, they likely did have more freedom (plus it meant they got to keep their lives). Since, as Halsall notes, the laeti were widespread throughout the Empire, it would seem that large numbers of barbarians willingly surrendered to Rome after being defeated in battle. This probably means that these men also knew that there was a chance that they would be allowed to settle as laeti, rather than simply executed.

There was also the possibility that these men would be "drafted" into the Roman army after surrendering or being captured, which would be a good alternative to death for a lot of people. A great example of this is the army of Radagaisus, who was a Goth that invaded Italy in 405. Approximately 12,000 of these men were conscripted by the Romans after Radagaisus was captured and executed in 406. In addition to not being executed, barbarians who served in the Roman army were granted citizenship after their terms of service ended. Once they were given citizenship they were often seen as Romans rather than barbarians. In this case, though not in the specific case of Radagaisus' men, surrender was absolutely a better alternative than fighting to the death, as it gave you a path to Roman citizenship.

Sources: Guy Halsall, Barbarian Migration and the Roman West 376-568.