In the SRD's bestiary, most outsiders have an alignment listed. In D&D 5e celestials and devils are locked into their alignment - if they change they become something else. That made me curious about what happens to an outsider who changes alignment in Pathfinder.
The result doesn't necessarily have to be changing what kind of creature it is, it can be anything except for obvious stuff like personality changes.
Arueshalae is a good example of this. She is a succubus that Desna helped redeem. Despite becoming chaotic good, she remains a succubus.
Tabris is another good example. He was charged with the task of studying the multiverse and in doing so created The Book of the Damned. This study of the multiverse caused him to change from Lawful Good to True Neutral for his alignment and be exiled from Heaven, but he is still an angel.
Note: Both of these alignment shifts were accompanied by shifts in the personality of the beings causing them to act differently from how a normal member of their race would.
This GM says it would depend on how they gained their current outsider status.
In the first case they have known nothing before what they are and therefore likely nothing (as @william-porter has already answered) should happen with regards to their race or abilities. The Elemental Princes and Princesses, such as Sunnis and Yan-C-Bin, would seem to be prime examples of this.
In the second case the outsider formed is usually a petitioner or lowest rank creature on the plane aligned with the mortals (former) alignment. This GM would put Arueshalae in this category since pure-blood demons are mortal souls* corrupted and risen through the ranks of the Demonic hierarchy. So Arueshalae might be redeemed back to (at best) a demon-blood-free mortal who would be free to do anything a mortal can do (including be good in life, die, go to heaven, and rise through the Divine ranks to be an Angel/Archon or whatever fits best). The fact that she still has all her Succubus powers makes me think she still has a long way to go! Which will be in all likelihood be an epic story. :)
(* Except where they fall into the third case.)
In the third case we're dealing with outsiders sliding along the alignment axes. Law to Chaos and Good to Evil, and vice versa. Tabris looks to have slid on both axes, but only halfway on each. So it kind of makes sense he has kept his previous racial/divine-rank powers because he's right in the centre of all the choices where all are equally applicable so the least amount of work the multiverse has to do is to let him keep what he's got.
This is pretty murky territory admittedly, but one example which appears to be in this category are the Erinyes Devils. Some, not all, just some, of their number are actually fallen angels who have descended. It is implied in the PathFinder Bestiary that this is possibly how the Devil rank of Erinyes was originally formed. It is why their wings are feathers not bat/dragon-like as the rest of Devilkind. Let's consider an Erinyes who is one of the fallen for a moment, they can theoretically ascend back to their Celestial status in which case should they not be restored with the abilities of their divine rank? This GM thinks it would be logical to assume so. First comes the alignment change with the personality change (these may be gradual), but at some point you have to start switching out Infernal powers with Divine ones. I speak from experience, so believe me when I say this can be be complicated!
