MySQL Database Missing on UNIX server. Possible to recover?

My dedicated server is VERY old (running Apache/1.3.37 (Unix) PHP/4.4.4 FrontPage/5.0.2.2510).

We have a script that runs and manages our customer database. Early in the morning last Friday, it was working fine and processed data as usual. Later in the day, we got this error:

Cannot connect to MySQL: Can't connect to local MySQL server through socket '/tmp/mysql.sock' (111)

We contacted support (which is minimal since its a dedicated server) and they told us:

"The server is compromised and the operating system would need to be re-imaged. me clients have been reluctant to upgrade for various reasons, and now we're in a situation where the known vulnerabilities are being exploited. The issue with the server is that MySQL is broken and is missing critical system files."

When we went in via Putty to retrieve the database, the folder that I believe it should be in was empty (I should add that they did a reboot)

Is the data lost? Is there a way to retrieve it? Unfortunately, the last full backup I ran on it was a year ago. While that's better than nothing, I'm hoping there is something that can be done to get the current copy.