W2 to a 1099

Yes--IF the nature of your work and working relationship has changed so that you are in fact a 1099 "employee," which is properly called an independent contractor. (Note: independent contractors are NOT actually employees; they are more akin to a separate business, like a vendor, paid to do something for their "employer.") The law is very clear: it does not matter what you call someone--the nature of how they work for you determines whether they are an employee (what you call a W2 employee) or an independent contractor (what you call a 1099 employee). If someone works in such a way that they are an employee, not independent contractor, they are an employee and must be paid on a W2; the employer must pay the employer portion of social security and Medicare taxes; if hourly, the employee gets overtime; he or she would be eligible for unemployment benefits and possibly for FMLA leave; etc.
Again: the reality matters, not the name the employer chooses to give the worker. The IRS's website has a good discussion of the difference between employees and independent contractors (when someone is one or the other), but in brief, if your employer sets your hours, can manage or direct you in how you do your job, and can tell you what location(s) you must work at, you are almost certainly an employee (W2), not independent contractor (1099).
Now, if you do in fact meet the criteria to be an independent contractor, they can choose to pay you on that basis.