Running Java in "Unsafe mode"
It looks like unsafe mode allows the Java app full access to your filesystem, which is enough that a malicious Java app could do anything it wants (take over your computer, infect it with malware, spy on you, etc.).  So, the name "unsafe mode" does seem appropriate here.

It's your call whether you want to take the risk.  Personally, I wouldn't, on my own personal computer.  I might set up a virtual machine and run the VPN client inside the VM, or ask the client for another solution that doesn't involve shooting holes in your computer's security.  Right now, Java security is a bit of a mess; it's a shame we don't have better solutions available.