For your argument to make sense, you would have to show that undocumented aliens' contributions are akl that's s standing between Social Security and failure. Got any actual figures to share with us?
And there is a simple solution to ensuring that Social Security will always be able to pay out the benefits that it owes: remove the income cap.
"Raising the tax cap could increase higher earners’ benefits as well, depending on how policymakers treated newly taxed earnings. Changes to the tax cap could close roughly a quarter to nearly nine-tenths of Social Security’s solvency gap, depending on how they were structured."
https://www.cbpp.org/research/social-security/increasing-payroll-taxes-would-strengthen-social-security#:~:text=Eliminating the cap would make,higher earners would pay more.
And if you dismantle payroll tax avoidance schemes such as subchapter S corporations, which are there to benefit the wealthiest 10%, Social Security would be rolling in dough. Or subject stock option incentives to SS tax. Or, heaven forbid, treating capital gains just like earned income.