Summary: If collecting anything from a taxpayer will cause him financial hardship, the IRS cannot collect and will place a taxpayer into the "CNC Tax Program." The catch: the IRS decides if it is financial hardship.
If collecting any money at all from a taxpayer would cause him/her to suffer from financial hardship, then the IRS is required - by its own regulations - to place the taxpayer in what is referred to as "Currently Not Collectible" (CNC) status. When a taxpayer is placed in this status, the IRS will generally not take any collection action against the taxpayer for at least 2 years. If the IRS decides to take a taxpayer out of CNC status, then the IRS will send a letter.
While CNC status is mandated by IRS guidelines in certain scenarios, that does not mean that the IRS will take your word for it, and it does not mean that the IRS will follow its own procedures. The IRS will most likely ask for documentation to support what you claim are your finances. However, depending on the amount you owe, or the amount of your income, the documentation request may be limited in scope.
Note: A similar rationale (financial hardship) that is applied for CNC status is also applied when the IRS is considering whether or not to return/release levied funds to a taxpayer. Speak with a professional for more information.