Hi [mention:4187e9f2c0404e4aa25182e3f69c4c03:e9ed411860ed4f2ba0265705b8793d05]
From my point of view the 2nd option( Run as whoever designed this process model) is better because process models initiated by a user x are having its running instances and before these instances get completed the account for user x gets deactivated then all those process instances started by user x will break, so to avoid such situation I would recommend you to configure 2nd option in swimlane assignment properties.