The error is telling you that the length of the subject is too big to fit into the subject field in the database.
To fix this simply:
With your handy dandy MySQL client tool (MySQL Workbench, or MySQL Admin) go into the database. Take a look at the ost_ticket table. Change the attributes for the column "subject" to VARCHAR(255).
Note: You might want to change the email, name, subject, and helptopic while you are in there as well. It's been a while, and I forget the default size of those, but on my implementation they are all 255.
Note2: This *SHOULD* be plenty long enough unless you work with people who don't understand how to use email. We have some people here that put their entire body of their email into the subject (which I find strongly annoying). This change will make it so that the allowed size is 255 characters. If that is not long enough for your users, the next step up from VARCHAR(255) is TEXT. TEXT will store something like 65000 characters. Generally speaking you want to use the type and size of data that you want to store in the database in applications. MS Outlook used to (not sure if it still does) limit the Subject to 255 characters also. Sadly RFC 2822 does not have a limit on the size of the subject field.
Lastly to determine which database the installation is using check out the contents of the
SiteDir/include/settings.php
Where SiteDir is the main directory of the OST install. On or about line 40 is the DBNAME, DBUSER, and DBPASS that the previous employee used during installation.
Hope that solves your problem. :)