checkout the remote stable branch
git fetch <remote> <branch>
Your local repo will now have a read only copy of the remote tracking branch, now check out to the read only tracking branch
git checkout origin/<branch_name>
Your VCS (whatever you are using) will start show messages like:
HEAD is in a detached state
Previous HEAD position was c293198
And the current branch as a hash fragment like
All detached HEAD means is that making a new commit, then moving away from it (by checking out something else) will leave you with no reference to that new commit.
checkout and create the new "feature" branch from the remote tracking branch
git checkout -b "feature_branch_intended_for_remote"
At this point any commits will be added to this totally new branch - whose history was the original stable.
This means, you got the data of the remote stable (which you could not modify) and at no point did you create a local working copy of the upstream stable - which you might accidentally push back upstream.
So now you can now
- commit your work into this new branch
- push it back to the origin as a completely new branch
git push [--set-upstream | --track | -u] <remote> <feature_branch_intended_for_remote>