Should the undead be eligible to hold public office?

We’ve got rules about who can hold public office and even more about who’s eligible for the highest office. We know someone that’s already served two terms as president is ineligible, but what about someone that’s already had their ticket punched? Is public office something that should be open to those on both side of the grave, (provided they can get their party’s nomination or raise the funds to run independently) or is it too much for the undead to expect these sorts of career paths to be open for them?