See the Ripple Trust Lines topics in the Ripple forum.
In this context "empty trust line" probably means a trust line with a zero balance but a non-zero limit. Such a line indicates to Ripple that you are willing to accept a balance of the specified currency from the specified issuer.
Note that the forum topic you refer to was written before the client added support for the server-side "no rippling" flag. This is implemented backwards in the client as an "Allow Rippling" checkbox which is not checked by default. What that means is that if you use the default to create two trust lines the Ripple system will not allow funds to "ripple" between them. Trust lines created before this option was present, or created with the checkbox selected, are allowed to "ripple"; you overall balance will stay the same but it can move (within the trust limits set) to/from a trust line that has "Allow Rippling" enabled. This is an incredibly powerful and useful feature.
So in short the "scam" is to get someone to foolishly extend a trust line to an account the attacker controls for a currency that they hold a balance on (or will in the future hold a balance on) and have the user check "Allow Rippling" on at least one of those trust lines. Then the attacker can make a payment that "ripples" through the victims account "taking" their positive balance and replacing it with a worthless balance they have no intention of redeeming.
To avoid this simply do any one of the following:
Only ever add a trust line to a Ripple account that you trust. Don't tell Ripple you trust someone that is untrustworthy. Only set the limit to an amount you're willing to risk.
This is incredibly basic and obvious but sadly there are people willing to blindly follow pretty "click here" picture instructions to do all kind of unsafe things to their accounts. There is no reasonable technical measure to protect these people from themselves. An attacker could just as easily claim they need your Ripple secret or your pass-phrase in order to send you a payment and some non-zero number of people will foolishly give away complete access to their account.
Leave the "Allow Rippling" checkbox unchecked unless you know what you're doing.
Or even more simply: don't randomly click things or make changes you don't understand on a system that involves your money just cause some random place on the internet tells you to.