I disagree. Penelope was characterized from the beginning (as in Sly 3) as someone who lies about her identity for monetary gain.
I guess I have a different opinion than many fans. At first, I disliked the twist of Penelope betraying the gang, but now, I really like it.
We know that Penelope was a liar from the beginning; she "photoshopped" her avatar on ThiefNet to be more attractive and masked her identity in order to bypass the age laws associated with dogfights (Bentley "photoshopped" his avatar as well, but that was because he was ashamed of his physical disability rather than a lack of feeling attractive). We also know that she is attracted to power and money over all else. Sly was attractive to her because he beat her at her own game, but once Bentley, who is more intelligent than Sly and therefore is more likely to provide her with power and money, saved her, she gets over her slight crush on Sly, going to someone who, for all intents and purposes, is the most powerful person(?) in the group. This is backed up when in Thieves in Time Bentley not only saves Sly (who was until that moment, helpless to save himself) from Penelope, but also lifts the rubble from the giant mech suit off of his leg.
Le Paradox, as Penelope said, was just a means to an end. A way to make money when Bentley refused to be a "normal" thief, or even sell weaponry. At the end when she sends postcards to Bentley, she may be trying to lure him back in, creating a trail of breadcrumbs that, if decoded, would lead right to her. What would happen then? Would she attempt to rejoin the gang by lying about what she had done or why she had done it? Or would she try to destroy Bentley?
I wrote that on the Sly Cooper subreddit in response to similar questions and discussion.