Hello friends,

I got my Green card through self petition 3 years ago while working full time for a company. I had provided them details about my status change then and now after 3 years, they tell me that my FICA taxes were never taken off and I have to pay the unpaid FICA taxes of the last three years which comes down to 25k+. What happens if I don't pay those taxes, will there be an penalty or interest over time?

Thanks.

U gotta pay what u gotta pay. Maximum penalty is jail time and revocation of green card and finally deportation .

Set a payment paln and pay , interest will only accumulate upto 14% max . 14% on 25 k will be huge.

I curious on this matter.
If you have work in any company with W2 the company is responsible for FICA ,SS and state if taxable ( 10 states do not file state tax)
Did you do your own tax or got help ? How did you file tax those years and it did not flag ?
If you work as a contractor then you will be responsible and must be getting 1099 misc income ( line 7) and while filing taxes you have to use Schedule C and without paying that FICA and SS your tax filing is incomplete.

It means you have not filing taxes otherwise these problem would not come to hunt you. If you live in us , maintain visa and keep paying axes. May be you outsmarted yourself? 
There is a saying ,
Jaisi karani waisi bharani.