Some time ago Sitecore extended the database tables that do not have clustered indexes with the DAC_Clustered index, based on the DAC_Index table column.
This was done in order to enable the creation of DACPAC/BACPAC files for further deploying to Azure SQL.
Since this index is a non-unique one, the Database Engine automatically adds a 4-byte uniqueifier column to the table for internal purposes.
Due to the fact that the DAC_Index column contains the same NULL value for all table rows, the index uniqueifier gets incremented for each following row.
When the index uniqueifier value gets higher than the max int size (2147483647), an error similar to the following occurs when inserting a new entry into the table:
System.Data.SqlClient.SqlException: The maximum system-generated unique value for a duplicate group was exceeded for index with partition ID 72057623183360000. Dropping and re-creating the index may resolve this; otherwise, use another clustering key. at System.Data.SqlClient.SqlConnection.OnError(SqlException exception, Boolean breakConnection, Action`1 wrapCloseInAction) at System.Data.SqlClient.TdsParser.ThrowExceptionAndWarning(TdsParserStateObject stateObj, Boolean callerHasConnectionLock, Boolean asyncClose) at System.Data.SqlClient.TdsParser.TryRun(RunBehavior runBehavior, SqlCommand cmdHandler, SqlDataReader dataStream, BulkCopySimpleResultSet bulkCopyHandler, TdsParserStateObject stateObj, Boolean& dataReady) at System.Data.SqlClient.SqlCommand.RunExecuteNonQueryTds(String methodName, Boolean async, Int32 timeout, Boolean asyncWrite) at System.Data.SqlClient.SqlCommand.InternalExecuteNonQuery(TaskCompletionSource`1 completion, String methodName, Boolean sendToPipe, Int32 timeout, Boolean asyncWrite) at System.Data.SqlClient.SqlCommand.ExecuteNonQuery()
Find more details about clustered indexes here: Clustered Index Design Guidelines.
For the on-premise solutions remove the DAC_Clustered index from the affected table.
Contact Sitecore Support for the help in case the error happens on the off-premise solution.