I simply meant that when the government issues the official statistic it never includes such people.
The govt. releases their own U6. Of course you have to dig around to find it and the Obama propaganda machine known as the MSM isn't going to report on it but it's out there. Think it's on the BLS website.
does that include the number of people who ran out of unemployment benefits and the number of people who didn't apply for unemployment after losing their jobs?
Yes.
From wikipedia:
The BLS also calculates six alternate measures of unemployment, U1 through U6, that measure different aspects of unemployment:[81]
U1: Percentage of labour force unemployed 15 weeks or longer.
U2: Percentage of labour force who lost jobs or completed temporary work.
U3: Official unemployment rate per the ILO definition occurs when people are without jobs and they have actively looked for work within the past four weeks.[2]
U4: U3 + "discouraged workers", or those who have stopped looking for work because current economic conditions make them believe that no work is available for them.
U5: U4 + other "marginally attached workers", or "loosely attached workers", or those who "would like" and are able to work, but have not looked for work recently.
U6: U5 + Part time workers who want to work full time, but cannot due to economic reasons (underemployment).
U3 is the measuring stick as it allows country-by-country comparison.