How to specify a SQL Server maintenance plan subtask to run unconditionally on success or failure of preceding tasks?
There are 3 options in Value: Success, Failure and Completion (approximate). Changing the value to Completion for all the preceding precedence constraints should ensure that the backup task is reached regardless of the upstream tasks.


  Execution Results
  
  The precedence constraint can use the following execution results alone or in combination with an expression. 
  
  
  Completion requires only that the precedence executable has completed, without regard to outcome, in order for the constrained executable to run. 
  Success requires that the precedence executable must complete successfully for the constrained executable to run. 
  Failure requires that the precedence executable fail for the constrained executable to run.
  


Further reading:


https://www.simple-talk.com/sql/ssis/working-with-precedence-constraints-in-sql-server-integration-services/
http://technet.microsoft.com/en-us/library/ms141261.aspx
http://sqlblog.com/blogs/jamie_thomson/archive/2009/10/11/things-you-might-not-know-about-precedence-constraints-ssis.aspx
http://blogs.msdn.com/b/mattm/archive/2006/10/30/using-expression-based-constraints.aspx