Keeping in mind that Valerian's troops were hit hard by plague in 260, and despite his recent victory near Edessa, Valerian I decided to try his hand at some good old fashion negotiation. It didn't work out that well for him.
Valerian I, along with his top men, were captured by the Sassanian King Shapur I, somewhere between April and July of 260. Shapur had no intention of negotiating, and took Valerian I captive.
Now, on to what happened to him after he was captured. Things get a little sketchy as far as when he died, but we do have some accounts as to what happened to him while in captivity, and it isn't pretty.
Valerian I was used by Shapur, basically, as a living trophy. He is said to have used the aging emperor as a stepping stool when mounting his horse. When not being tortured and humiliated, it is said that he was kept in a small cage.
The history then goes; after his death his skin was removed, dyed, stuffed and preserved and was kept on display at the Royal Palace for a very long time. It would make for an interesting archeological find!
Briefly, regarding your question as to how emperors or ranking officials were treated when captured, this story is a good example of how it was done during the 3rd century. Valerian I had fought some of the toughest warriors around, and for the most part was very successful. He got a bad rap from later Christian writers, but he deserves much more credit than he has gotten over the centuries.
Source: Coinage and History of the Roman Empire, volume one, David Vagi.