Two ways to find out:
1) in the search function, type a member's name, click on "by poster" in the drop-down menu;
2) or click on their name at the end of their posts.
Either way, an active member's posts will appear, but if they've been given a time-out, a page comes up stating, "This account has been banned or suspended."
As far as I know, if a member actually gets banned, all their posts are removed as well, so if their posts still appear in the threads, they've only been suspended.
I don't know which post got him booted - considering the sort of thing he posts every day, it's hard to imagine that one post was more out of line than any other, especially since his whole modus operandi involves personal attacks and racist innuendo. But the guy has nine lives around here, so I imagine he'll be back before next weekend.
Correction: the second method I described only takes you to the member's profile page.
"As far as I know, if a member actually gets banned, all their posts are removed as well, so if their posts still appear in the threads, they've only been suspended."
Wow! They just don't kick a person out...they erase their entire history as well? Ruthless! Seems a little unnecessary, but da rules are da rules.