What makes them "not real?" The same basic definition has been used in the US for about 90 years, and is used for almost every country in the world. Sure, people often use a more informal definition of "unemployed" in conversation, but that doesn't make it the "real definition."
Those numbers are published. What do you mean by "gone beyond an artificial deadline? There's no time limit to be classified as Unemployed. There's no list either, so no one can be wiped off it. And why do you think someone who is not trying to work should be classified as Unemployed? That's what unemployed means...Unable to find work. If someone's not looking for work, we can't know if they are able or unable to find work.
But if you want the breakdown of the population...no problem.
One caveat: The Labor Force Statistics only include people in the 50 states and the District of Columbia who are 16 years old or older, not active duty military and not in an institution (prison, mental institute, old age home etc).
Using the Not Seasonally Adjusted numbers:
Adult Civilian Non-Institutional Population: 244,995,000
Labor Force (Employed plus Unemployed): 154,512,000
Employed: 142,698,000
Unemployed (willing, available, actively looked for work previous 4 weeks): 11,815,000
Not in the Labor Force (not working or looking): 90,483,000
Do Not Want a Job: 84,084,000
Want a Job: 6,399,000
Did Not Search for Work in Previous Year: 3,417,000
Searched in previous year but not past 4 weeks: 2,982,000
Not Available for work: 656,000
Marginally Attached (available now): 2,326,000
Discouraged: 803,000
Reasons Other than Discouragement (personal reasons for not looking): 1,523,000
So what are the "real numbers?" These are monthly numbers so it's about what people were doing between February and March. If someone hasn't looked for work in that time period, what does that tell us about how easy/hard it is to get a job in that time period? What does someone who didn't get hired in March but who says that they could not have accepted a job if offered tell us?
Sources:
Defintions:
Table A-13
Table A-38