Personally, I like the idea of an abandoned character category. I don't like having to wade through eighty characters who don't want to play anymore every time I want to go look at who's active. It sends a bad message. And frankly, if they're not playing, screw 'em.
In general, if you're looking for parties based on the Approved Characters list, you're probably already wasting time. It doesn't list anything but a name, so you have to open each character individually just to find out what class, race, and level he or she is.
The Adventures page, OTOH, gives you a snapshot (both a literal image if one's there, and a list of classes and levels) of each character when you're perusing, and as noted before, is more or less filtered on activity.
Given that, I'm with SK in thinking that 'abandoned characters' may have a feel of booting players. Especially in PBP, I've seen a lot of folks fall into long lulls of inactivity for perfectly valid reasons (sometimes unforeseen--and thus without warning) only to come back even more involved than ever when they return; having to sheepishly ask someone how to become 'unabandoned,' though, might make those returners feel stigmatized. It's also entirely possible I'm assuming thinner skins than most folks have.
If the concern is that someone coming in will go through the approved characters list and think we're mostly inactive due to how many approved-but-inactive characters there are, I'm not sure calling them all out on a separate page helps perceptions on attrition or what have you.
If we're looking at giving newcomers a better picture of our activity level, maybe a front page change would be an option: If we rename the Adventures page something like "Active and Adventuring" and take out the "approved characters" link in the Players Guide section, that might better point folks where we want them to look for the characters / players they can expect.