Processing keeps happening on the partition with quorum.
A practical example I worked on is Google's Photon; multi-region logjoining with Paxos for consistency. When the network caused a region to become unavailable all the logjoining work happened in the other regions. Resources were provisioned for enough excess capacity to run at full speed in the case of a single region failure and the N-region processing allowed the redundancy cost to be as low as 100%/N overhead.