If they didn't steal your withholding, it depends a great deal. But if your employer stole your withholding, the IRS will sue them on your behalf. You will absolutely have grounds to sue them, and because tax law is so cut and dried in these situations, in that case, you will almost certainly win.
You need to contact the IRS immediately and advise them what your employer has done. This is more important than anything else because until you do, you can't be sure the IRS will figure out what happened (they might. They're really good at tax stuff).
If your employer didn't advise you that you are now responsible for paying your own quarterly estimated income taxes, the IRS will almost certainly grant you relief from penalties for failure to file timely and they could potentially abate interest as well, depending on the circumstances. They are especially likely to grant penalty and possibly interest abatement if you've never filed 1099 before.
If your employer withheld tax from your pay that they then failed to turn over to the IRS, good news for you - bad news for them. The IRS takes no mercy whatsoever on employers who steal tax withholding from employees. Advising the IRS that this may have been the case is all you should need to do - the IRS can check its own records, your employer's records, etc. They will let you know once they've determined whether your money is where it's supposed to be; if anything is out of order, rest assured they will already be pursuing the case against your employer. In this case, the IRS will waive all penalties and interest that may have been assessed as a consequence of your employer's failure to turn over your withholding.
If you are currently unable to pay, that's not the end of the world. Make the IRS aware of your current financial circumstances and your inability to pay due to unemployment. They have installment agreements you can request, or if that won't work, they can temporarily suspend collection action while you get things straightened out. There's a bunch of paperwork they'll ask for, and penalties and interest will continue to accrue, but as long as you let them know the situation, they will apply a dramatically reduced rate to reflect your efforts to comply.