Dithered Negation

Today's Blondie features a very odd threat from Mr Dithers:



Hmmm. Clearly Mr Dithers means "work part-time or I'll stop paying you" but is that what he said?

You will lose the benefit of not having your paycheck stopped.

This only works if it's "without benefits" - it's a problem with over negation. Imagine him saying "you have to work part time". If Dagwood said, "But with benefits?", then "Benefits like not stopping payment on your last paycheck" would work. Here, not getting paid is what they won't have, which must mean that getting paid is what they will have. Yet, we know that's not what he meant.

How is it that pragmatics so easily override syntax? It's fascinating.