Runtime.getRuntime().addShutdownHook(new Thread()
{
    @Override
    public void run()
    {
        updateZonas();
        db.close();
    }
});

This works for any Java application(Swing/AWT/Console)

I think I found cause of this behaviour (at least on linux distribution).

ProcessHandle.Info object is created with following method:

public static ProcessHandle.Info info(long pid, long startTime) {
    Info info = new Info();
    info.info0(pid);
    if (startTime != info.startTime) {
        info.command = null;
        info.arguments = null;
        info.startTime = -1L;
        info.totalTime = -1L;
        info.user = null;
    }
    return info;
}

where info.info0(pid) is call to native method. So I've downloaded openjdk source code and checked this method implementation. On linux JVM retrieves process data by reading /proc/{pid}/stat,/proc/{pid}/cmdline, /proc/{pid}/exe which are no longer available after process termination.

To answer my question:

There is no way to get ProcessHandle.Info for finished process.

Use Runtime.getRuntime().addShutdownHook(Thread).