I deleted the original basket on my forum years ago when I joined, not realizing it's function on the site.

Having the forums become cluttered up with a ton of locked threads (due to post count being maxed) that split from the original, is there a way I can set up a new basket so that when threads split and the old one locks, it automatically moves to the basket?

Hi, yes it's possible. Simply create a new forum and call it whatever you'd like and set whatever permissions you'd like. Then, once you've done that go to:

1. Administration Panel (advanced mode)
2. General Tab
3. Configuration (on the left, under Forum)
4. Select the forum you've just created for 'Basket'