This GM says it would depend on how they gained their current outsider status.
- Were they born that way, such as Elementals, Githyanki, Tiefling?
- Did they pass through death's door, such as mortals do?
- Did they evolve or devolve from some other creature/race?
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!