Can an employer use W-4 to withhold taxes and give employee a 1099?

No. A 1099 is issued to self-employed contractors hired to do a job. If your employer issued you a 1099, they are telling your state's Dept of Employment and Dept of Revenue that you're an independent contractor (self-employed). This means they generally are not withholding any taxes from your pay, nor are they paying their share of payroll taxes or paying unemployment insurance for you. This puts you on the hook for all your own self-employment taxes (FICA & Medicare) which is shared between an employer and an employee. You'll want to check on independent contractor laws in your state to see if your appropriately classified and your employer is paying what they're supposed to pay.