First of all, lying on your taxes is illegal. Don't do it.
Secondly, I doubt that reporting fake self-employment income would be a good financial move even if there was zero chance of being caught. Social security benefits are calculated on a tiered system based on your lifetime wage income. See
this document for the specifics of how you calculate it for someone who turned 62 this year. In a nutshell, you list out how much you earned each year and multiply each year's earnings by a scaling factor to convert it into current year dollars. You then take the highest 35 years (or all of the years you worked if it's less than 35) and add it up.
If this inflation-adjusted lifetime earnings number is under $347k, each additional $1,000 of lifetime earnings will increase monthly benefits (at "full retirement age") by $2.14.
Between $347k and $2.09 million, each additional $1,000 of lifetime earnings will increase monthly benefits by 76¢.
Over $2.09 million, each additional $1,000 of lifetime earnings will increase monthly benefits by 36¢.
Let's suppose your parents are each in this middle bucket of lifetime earnings, and let's also suppose that their real income puts them in the middle of the 15% tax bracket. If they claim an additional $80k of fake self-employment income, they'll pay about 20% federal income tax on this money (some in the 15% bracket and some in the 25% bracket), plus another 15% for self-employment taxes. Let's call it $28,000 of taxes, give or take. In exchange for that $28,000 of taxes, they'll get about $60/month if they start taking social security at their "full retirement age" (67 if they were born in 1960 or later).
If they invest that $28,000 instead, the 4% rule says they can safely withdraw $93/month starting right now! No waiting until 67 needed.