U6 (currently at 7,7%) includes all of the following: "People marginally attached to the labor force are those who currently are neither working nor looking for work but indicate that they want and are available for a job and have looked for work sometime in the past 12 months.
These statistics come from a survey of households, so it's functionally non-representative to begin with because the data only comes from the kind of people who bother to answer surveys from the government. But more importantly, the methodology is shit:
People with jobs are employed.
People who are jobless, looking for a job, and available for work are unemployed.
The labor force is made up of the employed and the unemployed.
People who are neither employed nor unemployed are not in the labor force.
For one thing, those rules are INHERENTLY CONTRADICTORY because a person can have work and be seeking work at the same time; per these rules a person who is in this position has not been classified because they are both employed and unemployed. This is where we should go back to the drawing board because the BLS has outright told us that their methodology is broken, but:
The BLS is not counting the underemployed. The BLS doesn't know who "lost" their job (or it just turned out to be bullshit) between the time the survey was completed and the time the statistics were published. People are considered employed if they did any work at all for pay or profit during the survey reference week. This doesn't tell us whether they can actually meet their needs. No job should be allowed to exist which doesn't pay enough for an average person to meet needs if they do it full time, but plenty of such jobs have been allowed to exist, so this methodology is entirely insufficient and seemingly deliberately designed for falsehood.
Can we trust any other source? No. There is no trustworthy source of this information because employers are not required to report enough information to the government to have trustworthy information. This is also by design. And I'm not talking about motivations here, you can draw your own conclusions about that, but the system is literally not designed to collect that information and there's really no argument to be had about that.