So she wants the job badly enough to continue working for an employer and an accountant who are violating the law and cheating her?
For a $60,000 salary and assume monthly paychecks, her gross is $5000 per month. The employer must withhold $382.50 in social security and medicare, then the employer remits to the IRS on form 941, $765, representing the employee share and the employer share. If the employer is deducting the entire $765 that's illegal. It can be corrected by filing an amended form 941, and the deadline to correct it would be January 31, 2021 since that's when the W-2 is issued.
If it is not corrected, your wife can file a complaint with the state labor department for unfair wage practices, and possibly file a form SS-8 with the IRS.
If jobs are so scarce that your wife would prefer to continue working for someone who steals from her and doesn't care to fix it, I'm not sure I can offer any further intelligent advice. The minimum fair compensation, if she went to independent contractor status, would be $5382.50 per month, so that after your wife pays the SE tax, she nets the same $4617 that was the original bargain. If she agrees to work for a gross of $5000 per month, that's a pay cut from what was negotiated.
Making her independent would place all the compliance burden on her head, which might be good since she would not be subject to her employer's screw-ups, but it will cost you (and not just money. Your wife will have to spend considerable amount of time educating herself on taxes and record keeping for self-employed persons.). You would definitely want a written employment contract.
The plus side of being an independent contractor is that the employer can set performance goals but can't require that she work certain hours or a certain schedule -- if she meets those goals, she fulfills the contract. And if she meets the goals in less than 40 hours a week, she is free to take on additional clients in her own name. If the employer requires her to work a certain number of hours per week, or at a certain location, and forbids her from working for other clients, then she really is an employee and she should not tolerate any shenanigans.
