We're not told. Since the text gives the impression that these were believers from the Old Testament era, we can infer that their time on Earth was transitory, not permanent—that they were just a-passin’ through. Ephesians 4.8-10 seems to suggest that Jesus emptied the righteous side of Sheol after his death and led those people of faith to Paradise (Lk. 23.43). I would consider that those souls spent a little time on earth during the transition as a witness to the people of Jerusalem of the reality of the resurrection and of our future resurrection as well.

What happened to the souls that were raised after Jesus's resurrection?

matt 27:52-53 -- The tombs broke open, and the bodies of many saints who had fallen asleep were raised. After Jesus’ resurrection, when they had come out of the tombs, they entered the holy city and appeared to many people.

So...are they dead now? Or in Heaven? Or...?