Was your ancestor institutionalized for a short time or for the last few years of their life? If so, they might have died a distance from where they actually lived. Records of the actual institution may be closed, but there might be local court records of the institutionalization. People who were sent to institutions weren't always "crazy," but might have simply needed more care than the family could give.
And they might have been buried on the grounds of the institution--leaving no tombstone behind either.