Available is a persistent status by default...was it changed on your system?
Anyhow, the User Status Monitor Initiator fires every time a user changes status (so, not just when they log out). One of the outputs is
Logged In Indicator
A value of 1 (one) will be returned if the user is logged in, and a value of 0 (zero) if the user is not logged in.
So, you
could write a handler that looks for a <> 1 in that variable (Logged_In_Indicator) and also looks at their "Status_Text" variable to see if it is something you don't want for a logged-out user (like "At Lunch") and then change their status to "Gone Home"
That handler will run a lot...every time someone changes status...so if you have a large site it might not be beneficial.