Repairing a corrupt mssqlsystemresource database...
We know that mssqlsystemresource is another vital system database which is essential for normal operations of SQL Server. (Please refer to http://blog.consultdba.com/2010/03/note-on-resource-database.html for details). So if in an unlikely case if mssqlsystemresource gets corrupted, SQL Server will be unable to operate properly.
Unfortunately there is no direct way to repair mssqlsystemresource as it is not a standard database. However if you need to fix mssqlsystemresource, retrieve a copy of mssqlsystemresource.mdf and mssqlsystemresource.ndf which was backed up before the corruption and simply overwrite existing (corrupted) mssqlsystemresource.mdf and mssqlsystemresource.ndf with the (good) backed-up copies. This will immediately fix the issue. Please be advised that as mssqlsystemresource gets updated with SQL Server upgrade, it is highly recommended to backup mssqlsystemresource (mssqlsystemresource.mdf and mssqlsystemresource.ndf) before any upgrade procedure along with having a standard backup mechanism to regularly backup mssqlsystemresource.mdf and mssqlsystemresource.ndf with any other database as a part of DR solution.
In case if you do not have a backup of mssqlsystemresource, then you may copy mssqlsystemresource.mdf and mssqlsystemresource.ndf from another similar SQL Server and overwrite existing (corrupted) mssqlsystemresource.mdf and mssqlsystemresource.ndf with the (good) copies. (This SQL instance must be at the exactly same level (version number etc) with the corrupted instance). This will resolve the issue related to corrupted mssqlsystemresource. However if you need to execute this procedure, you must immediately arrange a regular backup mechanism of mssqlsystemresource database as a part of DR solution.