There were several waves of Hunnic people the Sasanians faced beginning with those known in the Latin sources as the Chionites but including the Kidarites and Hephthalites as well. The short story is that they did not resist them very well. From the limited sources we know of many campaigns in the east against the Huns and massive outlays for defensive infrastructures such as the Great Wall of Gorgan. The Hephthalite king Akhshunwar defeated Peroz I on three occasions. The last time, the Shahanshah was killed along with most of his army who fell into a ditch that had been set as a trap and the Hephthalites rampaged the empire until they were granted a massive tribute that almost bankrupted the empire and inspired Khosrau's financial reforms. The Hephthalites played kingmaker for much of the fifth century. They helped Peroz reach the throne initially as well as his son Kavadh (on two occasions). Some have suggested that some of the Parthian noble families under the Sasanians had actually entered alliances with the Hephthalites as well.

The sources for the eastern Sasanian Empire are a bit of a mess and so is the scholarship, mostly focused on really nitpicky numismatics and archaeological material. A new book covers the history of the eastern empire very well and I would recommend checking it out. Khodadad Rezakhani, ReOrienting the Sasanians (2017)