If they went into the recycle bin, "Deleted by" & "Deleted Date" is in the database and the recycle bin UI.
Otherwise... some actions are stored in the client's even viewer - but not many.
There are log tables in the database, in which the moving, renaming and deleting of files and directories is logged. The tables are the HistoryRename, HistoryMove, HistoryDelete. Maybe you will find information here. As far as I know, the records will be removed from the tables, if the files in the vault were destroyed.