When updating or deleting some value, ES will mark the current document as deleted and index the new document. The deleted value will still be available in the index, but will never get back from a search. Granted, if someone gets access to the underlying index files, he might be able to use some tool (Luke or similar) to view what's inside the index files and potentially see the deleted sensitive data.
The only way to guarantee that the documents marked as deleted are really deleted from the index segments, is to force a merge of the existing segments.
POST /myindex/_forcemerge?only_expunge_deletes=true
Be aware, though, that there is a setting called index.merge.policy.expunge_deletes_allowed
that defines a threshold below which the force merge doesn't happen. By default this threshold is set at 10%, so if you have less than 10% deleted documents, the force merge call won't do anything. You might need to lower the threshold in order for the deletion to happen... or maybe easier, make sure to not index sensitive information.