We know from Wind and Truth that Taln attempted to kill Cultivation, presumably using a weapon given to him by Kalak. We also know that he withstood torture on Braize for 4,500 years without ever breaking. This theory proposes that the weapon Taln used to attempt to kill Cultivation was a Dawnshard, which then imprinted on his soul, preventing him from breaking while on Braize.
Among the possibilities for the weapon that Taln could have used to try to kill Cultivation, the Dawnshards rank pretty high. Other than Nightblood, which didn't exist yet, the Dawnshards are the only weapons that we know of that have been used to kill a God. Some kind of anti-Investiture weapon might work as well, but I think we can be reasonable certain that those wouldn't have been around at that time either. There really isn't a candidate that we know of for a weapon that could have been used to harm a God at that time other than a Dawnshard. Additionally, we know that Taln's soul is warped from his attempt to kill Cultivation. While that warping need not necessarily have been caused by the weapon (for instance, it could have been caused by Cultivation's response), we know that holding a Dawnshard warps the soul. We've seen that warping manifest in Sigzil's and Hoid's Torments, preventing them from directly harming others.
I believe that Taln held a Dawnshard whose Torment made it so that he could not give in to his torture on Braize. There are several possibilities for a Dawnshard Command that would cause this torment. For instance, a Dawnshard with a Command similar to Honor's Intent might prevent him from breaking, as Taln swore an oath to protect Roshar at the founding of the Oathpact, and breaking might be seen as a violation of that oath. Or the Command may be related to protection itself, or to resolve. Either way, it seems plausible that of the two Dawnshards with unkown Commands, one might cause a torment that would have resulted in Taln being unable to break.
This theory seems to me to best explain what we know about Taln. A Dawnshard fits with the attempt to kill Cultivation and his having a warped soul. In addition, the fact that Taln never broke despite 4,500 years of torture seems unrealistic to me as the result of human willpower alone. I also like this theory because it gives the Heralds' betrayal of Taln a lot more bite. While the Heralds made their choice to transfer most of the Oathpact to Taln without consulting him, the plan essentially requires Taln's consent as well, assuming he can choose whether or not to break. It's not much of a betrayal if Taln can make the effects of the betrayal moot by choosing to break. But if he has no choice, if the other Heralds abandoned him to be tortured on Braize alone, knowing that he could never give in to stop it...that would be quite the betrayal indeed.
So, that's my theory. I'll note one potential counterargument, which is that Taln was given his weapon by Kalak, yet Kalak clearly does not suffer from a Torment that prevents him from breaking. I think there are two ways to explain this, the first being that Kalak led Taln to the Dawnshard without holding it himself, and the second that Kalak didn't hold the Dawnshard for long enough to be affected by the Torment. (I'm not sure how long one has to hold the Dawnshard to suffer a Torment.) I think this theory nicely explains what we know about Taln, and it puts a darker spin on his abandonment by the Heralds. Let me know what you all think!