The IRS has three years to audit a return. If they fail to do so in that timeframe, then that return is forever off-limits to the IRS. In the same way, they have 10 years to collect any unpaid taxes or penalties. Again, if they fail to do so, that amount is forever uncollectible.
However, the catch is that the past-due amount doesn't become collectible until the amount has been finalized, either because a return has been filed, an audit has been performed, or a late-payment penalty has been assessed. So even though the IRS only has 10 years to collect a finalized debt, none of a taxpayer's prior-year returns have been finalized yet if he hasn't filed them, even if the taxes are 20 years past due.
You can see the problem that this presents, then. It is highly unlikely that a taxpayer or his employers, vendors or clients have good financial records going back that far. Maybe the best he can come up with are his W-2s or 1099s, and even then he'd probably have to ask the IRS for copies.
Unless the taxpayer has records of his expenses for those years, there will also be almost no deductions available to him, other than ones pertaining to dependent children and so forth. It is doubtful he can verify mortgage interest, charitable donations, that sort of thing.
Another important thing to keep in mind is that penalties and interest stretching back that far can be very substantial. Even partial taxes still due can add up to a lot of money by the time you tack on 10+ years of interest and expenses. So it will be necessary to negotiate an amount with the IRS; they would probably be willing to settle for pennies on the dollar just to get current, but the taxpayer should hire an attorney, EA or someone with experience negotiating with the IRS to represent him.
Better yet, he should have paid his taxes correctly and on time, and avoided all these headaches in the first place!