That's an excessive over-simplification of my point. And to answer you: no, he doesn't become "worthless" to me (whatever that may mean), but I will stop paying him for his services.
The fact is that the healthiest situation for any society is for every member to be able to afford to meet their basic needs with a little extra income. This is clearly not possible through a purely free job market. 'Sacrificing' some of your income to maintain this society and permit mobility is in your best interests. Who's to say you won't be the next one fired, or your child?