I think if Java was to be exploited in Linux; due to the many locked down / - root (Admin - System) files/permissions basically the malcreant would be after your Bandwidth. To add to their Bot, or collective of compromised Computers, subtley 'leaking' Bandwidth, or CPU Cycles. As I understand,
compromised Linux Systems would indicate having Admin (root) Permissions;
where it shouldn't have such permissions...
If your a 'Home User', target would be to
gain privileges to steal a little Bandwidth; or as I said CPU Cycles.
Everything is locked down so tight breaking root priviledges/permissions seems the first step.In a Network situation, like a Company, Trojans may be more likely; searching out Passwords, Account numbers, General juicy info. Also stealing collective Bandwidth and Computing Power.
Honestly I'm just guessing. There is but a few Linux Viruses, as such ? Java is pretty conspicuous when active. As I haven't read any reports of anyone being specifically 'Exploited' by this Java Security hole, and haven't spent much time looking for that info; who knows ?
I'm not up with Linux sites dealing with Malware.So in General; Symptons to look out for;
Sluggish performance, your
Modem/Router lights are flashing but you're not knowingly sending or receiving data;
redirects to other pages than ones your intending to go to when Browsing online.
I dunno, just common sense.
Problem installing an Anti Virus scanner on Linux, you'll still just find Windows Viruses, which isn't much help 
I did a Virus scan yesterday and Avast! said my 'etc/hosts' file was a Virus.
I have tried adding entries to it, like:
"127.0.0.1 facebook.com", but I obviously don't understand how the
hosts file works on Linux, so I reset it to it's basic default, 127.0.0.1 localhost.localdomain.
I've seen my Son go to facebook so it obviously wasn't working
[
http://winhelp2002.mvps.org/hosts.htm -
http://www.putorius.net/2012/01/block-unwanted-advertisements-on.html ]
I use
Adblock in Firefox, and have a huge list [
https://easylist-downloads.adblockplus.org/exceptionrules.txt ] that I
subscribe to which
Automatically updates, "set it and forget it", so blocking Adds, Bad sites isn't a worry.
Also I'm running linux, clear all my Tracks from my Browser, and are invisible online, almost.
Internet security vulnerability Test: ShieldsUp ! https://www.grc.com/x/ne.dll?bh0bkyd2 Doesn't hurt to review youe Security from time to time anyway.You'd likely know if your Computer seems to be infected, although I've never had a Virus, MS, or otherwise, there are obvious symptoms. Blah, enough already ...
