Question regarding Grid column width

I have the following scenario:

A grid with two colums.
The first column shoud adapt its width to the content, the second column should take the rest of the available width.
So far this is no problem.

Now here comes the tricky part:
If the content of the second column is wider than the available width, only the available width should be used for that column, and the content be truncated with an ellipsis.
We absolutely need to avoid horizontal scrollbars here.
Only if the second column would get smaller than a defined minimum width, this minimum width should be used and a scrollbar would be tolerated.

Does anyone have an Idea for that?