seattlecyclone is (of course) correct; the IRS will catch it if your Dad doesn't report the sale because of the 1099-S (which you can probably find in their closing/escrow paperwork somewhere). The IRS will computer match against his SSN and send him a love letter if it's missing from his 8949 / Schedule D.
I personally take the position that it is perfectly acceptable in situations like this to adjust the basis for any home improvements made (see IRS Pub 523 for the appropriate examples and limitations) even if you don't have the receipts. If your parents spent $10K on granite countertops, then they're (usually) entitled to the basis adjustment of $10K. The caveat is, of course, if they get audited and cannot produce receipts to document the adjustment then the IRS auditor may (probably will) disallow the adjustment and they'd owe the additional taxes plus interest. The other caveat is that without the receipts you may have to reconstruct data based on memory and perhaps old bank records or similar and you need to be reasonable in your estimates. Bad record keeping is not tax evasion, although overestimating expenses without receipts would be (IMHO).
Another idea for you: Most people don't save purchase records that long, but certain closing costs on the *purchase* of the property are adjustments to basis in addition to certain closing costs on the *sale* of the property. See IRS Pub 523, Worksheet 2, Line 4.
The other obvious idea is for them to hold onto it until one or both pass away and the survivor or beneficiaries receive a step up in basis to current FMV. You've probably thought of that option already and it may not be viable. But depending on their life expectancies, state of residence, unrealized gain on the property, ability/inclination to borrow, it could pencil out to borrow against the home instead of sell. There are obvious risks to this idea also.
