After doing some testing and discussing things with Blastdav, I have come to the following:
When a member makes a reply post in a thread and also changes the subject title in their reply post, the "true" subject title for the thread will not change. If I were to change the subject title in my reply here to "Forest property", and I then posted my reply and then scrolled back to the top of thread, I would still notice the original thread title had not changed. Other members cannot change another member's thread title. Only the original poster of the thread can change their own thread title in their very first post or they may ask a staff person to change the thread title. If a member changes their own thread title, then they must announce it in the thread.
When I'm at the bottom of the forum and I click on the following: "View the most recent posts on the forum." and I backtrack through all the past posts, I can see all the different titles that members used when they made posts.
I'm going to have to ask that members stop adding and/or changing subject titles, and/or using the subject title text box to "have discussions" when they make a reply post as that will only confuse other members as to the original topic/subject of the thread and may make them go on a "wild goose chase" so to speak looking for other threads and subjects which don't exist.