If your employer did not withhold any FICA taxes on your Form W-2 or other tax documents, I will suggest you communicate with your employer to resolve the issues. Employers who do not comply with the employment tax laws may be subject to criminal and civil sanctions for willfully failing to pay employment taxes. For now, you will still file your 2019 tax return as usual. If things need to be changed on the tax documents, you can always amend later. I am attaching the following links for your references:
FICA withholding
Employer vs Employee responsibilities
@prtk05
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