You can do something like this.
Your left column stays at a fixed width and stays on the left. Meanwhile, the right column of the table adjusts to fit the width of the browser but stops shrinking at a certain point. Set a minimum width for the right one that.
In other words, your HTML would be something like this:
I am the left column.
I am the right column.
Your CSS would be something like this:
Here is a live example. I added background colors so you can tell what's happening more easily.