A 1099 can't be e-filed without a correct tax ID number (SSN or EIN) but one could be filed by mail if an appropriate explanation was attached.
More importantly, if you perform work for someone and they pay you, you are required to report your income and pay the correct tax, regardless of whether they issue a 1099. If you planned to work "under the table" and now they are issuing a 1099, that's just following the law.
You should have already reported this income on your tax return, even without the 1099. If they issue a 1099 late, the IRS may eventually send you a letter asking about the income, and you would reply that you already included it in your taxable income without the 1099.
