We really need better ways of measuring economic health. I could lose my six-figure job, turn around, and get hired on as a server at Applebee's for minimum wage, and the "unemployment" rate would stay the same. Not to mention that it doesn't include those not actively looking for work. Either way, "full employment" doesn't mean much unless you take into account whether people are actually able to live a stable lifes…
We have good metrics. The problem is the media seems to only ever look at one of them at a time but we need to look at several at once to get a more complete picture. Your scenario would be called out by median household income, or better median disposable household income. Even the good old GDP per capita covers your case. Workforce participation also can be valuable instead of or in addition to unemployment numbers…
This is why there needs to be some kind of safety net so that the economy is not a proxy for life and death. In the USA, if you run out of money, you are in real trouble. We need to decouple success/failure in the market from personal safety. You should be able to try opening a hot dog stand, have it tank, and still be able to eat and go to the doctor.