If a player no longer wants a character, they can opt to make that character "playerless" by posting on the updates board. This means that the player relinquishes all rights to that character and offers it up stipulation-free to other players. Anyone can take a character listed as "playerless" in the Player field and do whatever they like with it. To find playerless characters, search "playerless" in the Player field. Claim playerless characters on the updates board. You can make up any information not listed in the database (e.g. personality, history, appearance).
Adoptable characters are ones which anyone can adopt, with a few conditions attached. To find adoptable characters, simply search "adoptable" in the Player field. If you see a character you like, contact the person whose name is in brackets after "adoptable".