Valens was killed by the goths at Adrianople.

you're thinking of Valerian, captured by Persians yes, but by Sapor of the Sassanid dynasty in 260 AD and never heard of again. Rumours had it that while he remained alive he was used as a foot/mounting stool by the Sassanid emperor, and when dead he was stuffed and kept as a trophy.

The Parthians were overthrown by the Sassanids about 220AD.