Query on Linked Server in SQL Active-Passive
No extra configuration is needed for the linked server to work on
DB2 and that's one of the Benefits of a Failover Cluster
Instance:



  In case of a failure (hardware failures, operating system failures,
  application or service failures), or a planned upgrade, the resource
  group ownership is moved to another WSFC node. This process is
  transparent to the client or application connecting to SQL Server and
  this minimize the downtime the application or clients experience
  during a failure. [...]
  
  
  Zero reconfiguration of applications and clients during failovers
  



Yes, it will work automaticaly on DB1 when it fails back and the reason is that:



  Only one of the nodes in the FCI owns the WSFC resource group at a
  time.



In fact you must use that virtual ip address or network
name
in order for the failover to work transparently:



  An FCI runs in a WSFC resource group with one or more WSFC nodes. When
  the FCI starts up, one of the nodes assume ownership of the resource
  group and brings its SQL Server instance online. The resources owned
  by this node include:
  
  
  Network name
  IP address
  Shared disks
  SQL Server Database Engine service
  SQL Server Agent service
  SQL Server Analysis Services service, if installed
  One file share resource, if the FILESTREAM feature is installed
  




This image from Derek Seaman's IT Blog might help you understand it better:



You never configure your applications (or linked servers) to reference DB1 (NodeA) or DB2 (NodeB), you must always reference the virtual ip address or network name (VirtualNode1) and it shall transparently address the active node of the cluster.