All versions of Trillian support a special invisible status. When you mark yourself as invisible, you immediately sign off to everyone on your contact list but can continue to see the status of your contacts. Invisibility is a way to stay online and connected without letting people know you're available, and you can continue to send and receive messages as normal while invisible.
If you want to stay available to certain contacts even when going invisible, you can add them to your allow list and they will see you explicitly marked as invisible instead of offline. To add a contact to your allow list: