I would like to build on what Casiella said...
I'd also think that, in PF, non-player capsuleers could choose to submit themselves to the law in exchange for some sort of additional resources, like those who remain within the formal navies (cf. The Empyrean Age).
When I read the documents, I don't read them as saying that our characters are legally dead and can have no possessions outside of the CONCORD economy, nor that they literally have no connections back to their original factions (cf. "Her Painted Selves").
I think it is either one of two cases.
1) A capsuleer cuts off ties from their original nation. They become "legally dead" and accountable to CONCORD law and regulation only. Thus, they are only permitted to access the capsuleer areas of listed stations, only permitted to interact with planets as far as the CONCORD Planetary Development Treaty allows them too, and so on. These are the capsuleers that form the enigmatic section of society that is disconnected from everyone else.
2) A capsuleer may choose to submit to the law of their home country to the same degree as an ordinary citizen, but is also accountable to CONCORD as well. By choosing to submit, they will be privy to the same rights and liberties as the other citizens, including the right to own property outside capsuleerdom, the right to vote, the right to participate in any civil process and so on. Similarly, if they break the law, they will be prosecuted the same way as any other citizen, all falling in line with other CONCORD law. This accounts for capsuleers who are regarded as the "elite" of a society, including capsuleer politicians (eg. head of states for 3 of the 4 empires, capsuleer Senators, Holders, corporate CEOs) and military officers. Discretion would be advised still, however, as citizens would regard capsuleers in a myriad of polarized ways (Eg. in the Fed, perhaps either loved or hated, with little in-between. For Caldari, accepted as a dubious but essential part of the State etc)
Number 2 makes sense to me, and I play by this rule, but number 1 can equally apply. Jita 4-4 is a chronicle that identifies a capsuleer that talks about getting in trouble with the station authorities for inappropiate behaviour in the non-capsuleer area of the station. I just don't believe for one second that if a capsuleer walks into a planetside market and goes on a killling spree can they not expect to be prosecuted. The existence of "citizen-capsuleers" across PF further indicates we are not barred from taking this position.
Cf. Rhea and Jaidon Heavenbound.