Hi venn_ng, need to be careful when trying to use and interpret s parameters, especially in cases where you're considering putting things on the ports of the network which aren't 50 ohms.
You should review the basic definition of power waves a and b, and the scattering matrix s, from Kurokawa's paper:
Here, Zi is the characteristic impedance of the network. In theory one can choose Zi arbitrarily, and it can actually be different for each port of a network, but in practice we basically always use 50 ohms (because all of our test equipment happens to be set up for 50 ohms).
However, it's important to realize that the s parameters of a network do not depend on the impedances connected to its ports.
This is contradicted by a lot of references out there which are sloppy with their terminology. For example, if I take an ideal transmission line like yours and connect both ends to a VNA, I should measure |S11|=0 and |S21|=1. But if I disconnect one end of the cable from port 2 of the VNA, I will measure |S11|=1 and |S21|=0. And if I then connect the cable to various impedances (like 10 ohms or 100ohms) I will see the measured S11 change phase and magnitude.
But its incorrect to claim that the S11 or S21 of the cable is actually changing. Those are properties of the cable itself, and I'm not changing the cable. What the VNA measures is everything between its two ports, and when I disconnect the cable it no longer sees just the cable, but a big open circuit along with the cable. Therefore the results displayed by the VNA don't describe just the cable anymore. We have to be careful when discussing S parameters, and always include context on the experimental setup.
Also your comment about DC gain is another good inroad to understanding s parameters better. Voltage gain and S21 are only the same when all ports are terminated with their characteristic impedance. Therefore if your S21 is derived with a characteristic impedance of 50ohms at both ends (like it is in 99.99% of cases), but you terminate its ports with different impedances, you should expect your voltage gain and S21 to be different.