Neither the IRS or state will know about any itemized deductions or cost basis for equities sold. The taxpayer may believe that the "correct" amount of taxes have been paid, but until a tax return is filed that information isn't available.

Some basic reasons for filing promptly:
1.) Losing paperwork
How many people who are not organized enough to file a tax return will be able to find all of the paperwork in 3 years?
2.) Statue of limitations
Statue of limitations starts from when the tax return is filed.
3.) The IRS and state are going to calculate taxes due based on standard deduction and the full sale price of equities
As my favorite procasinator has proved, if you have anything more than the simpliest return, the IRS and your state will be contacting you. They can garnish your wages and if you still don't respond in time, they will keep it.