If you connect an ideal matched load to port 2, that will set \$a_2\$ to zero.
However, it's not always possible, or convenient, to get a load that's sufficiently accurate for your purposes. It depends what accuracy you want to work to, and what frequency you're using.
At very high frequencies, GHz, we often use a 'sliding load', which is an approximately matched load, that can be slid along a precision air-spaced coax, to change its electrical length (reflection angle) without changing the absolute reflection. The measurement software finds the centre of the circle that results as the load angle is changed, and this point becomes the effective reflection from a load ideally matched to the air-line.
Another method uses shorted or open sections of coax of different length. With these it's a case of generate enough equations for the unknowns, and solve them simultaneously. Again, the impedance of the coax becomes the effective load impedance with this method.
If you have a load that's not matched, but accurately known, it's still possible to put its value into the equations, and get a good measurement of the S parameters, when used in conjunction with at least two other reflection standards.
