I think Pegasus can do what you want.

Pegasus stores new messages as *.cnm files in the mailbox directory. Other folders (i.e. copies of sent messages) are stored in compound files + indexes.

Therefore, if you would write a filter rule that moves all new mail where subject <> "specificsubject" to a 'to be read' folder, your separate program could check for new *.cnm files that are at least 1 minute old (give the rule some time to do its work).
Another option is to write a rule that appends the message to a specific file somewhere on your system. Which is best depends on how flexible your 'separate program is'.

Writing filter rules is very straightforward with Pegasus - give it a try.

I have been trying to find an email program that will check my pop3 ssl yahoo plus email account.

I need to know if Pegasus can do the following things: 

IF subject line of email = "SPECIFICSUBJECT"
then save the email text of that email into a .txt file in a specific folder
endif

 If Pegasus could name the files using an ascending number structure, that would be great. Such as, 1.txt and 2.txt and 3.txt OR SPECIFICSUBJECT1.txt and SPECIFICSUBJECT2.txt

I need Pegasus Mail to do this without any user actions at all.
I have a separate program that is monitoring the specific folder(s) to see if new text files are being added.