What happens when a fork/network split occurs on the Stellar network?
Assuming people chose adequate quorum slices and the system has quorum intersection (which is how the system is intended to be used), then with Stellar's new consensus protocol, at least one of the two partitions would be unable to settle transactions for the duration of the network outage.

Stellar does allow for redundancy, in that validators can have multiple slices.  For example, a slice might consist of any 5 out of 7 validators spread across countries.  In that case, if the partitioned country has only 1 or 2 validators, the rest of the world can continue to make progress.

This kind of scenario is actually unavoidable.  You have to chose at most two out of Consistency, Availability, and Partition tolerance.  This is sometimes known as "Brewer's theorem" because Eric Brewer conjectured it and Seth Gilbert and Nancy Lynch subsequently proved it.  See: http://www.cs.luc.edu/~pld/353/gilbert_lynch_brewer_proof.pdf