As an independent contractor or 1099 worker, you are not automatically enrolled in the Massachusetts Paid Family Medical Leave program, as you would be if you were being paid as a W2 employee.
You can, however 'opt in' to the program. This involves making payments (calculated based on your income) into the fund directly. If you have paid into the fund for two out of the prior four quarters when you need leave, you should qualify for benefits if you are otherwise eligible for leave.
If you work for a small employer (fewer than 25 employees) the amount of direct contributions to PFML is the same as it would be if you were a W2 employee, though the tax consequences may be different. If your employer has 25 or more employees, they would be required to contribute some portion of the payment to PFML, but are not required to do so if you were properly classified as an independent contractor.