Let's say you have a feature branch based off a different feature branch. Someone force-pushes against that branch and now your branch cannot be merely rebased or even merged against that branch because all those mismatched commits end up being treated as if they're actually yours (when they weren't). A potential recourse is this:
git fetch <remote>
git rebase --onto <remote>/<upstream branch> \
<local feature branch>~N \
<local feature branch>The value of N is the number of commits in your local branch that are your extensions to that remote branch. So if you originally based off the remote branch and added 6 commits, N = 6.
The above command has the effect of being like using format-patch HEAD~6 to get the last 6 commits as a patch, then doing a hard reset of the local branch against the upstream remote, followed by finally using git am to apply those patches.
In either case, if your branch has already been pushed to the remote, you will have to force-push these changes over your own branch. If you know anyone is using your branch as an upstream base: be nice and let them know about the above command.