Even without the mistaken withholding instruction you describe, an employer/administrator often might encounter the problem of lacking enough pay for all the things an employee might do with it.
For example, consider a paymaster who must withhold for FICA taxes, three income taxes (Federal, State, and city or county), two or more unemployment and disability taxes, and might apply salary reductions for the employee’s portion for health coverage, a health flexible spending account, a dependent-care account, and a 401(k)/403(b)/457(b) elective deferral.
Some employers develop an internal hierarchy—sometimes written, often not—to sort out these and other competing demands on an employee’s pay.
Most concur that withholding taxes comes before any of the health, other welfare, and retirement benefits.
And within employee benefits, most prioritize maintaining health coverage over voluntary retirement savings.
While I’ve never seen the Treasury or its IRS publish anything on this point, it should be unseemly for the IRS to assert as a tax-disqualifying operational defect an employer/administrator’s failure to apply perfectly an employee’s elective-deferral election if the reason was properly withholding taxes, especially any Federal tax.
About coordinating wage reductions across the many employee benefits and providing it in or under the plans’ governing documents, that’s possible when one law firm works on all plans of the employer. It’s hard to do using IRS-preapproved and other documents that come from the plans’ service providers. And even employers that use custom documents for all or most of the plans often don’t want to pay for the time it would take to do this right.