Upvote:8
The airlines are contractually obligated to transport you to your destination stations (usually an airport but a train station is also possible).
Keep in mind, a Stopover is different from a Connection.
So, if you're flying from New York to Los Angeles and book JFK-PHX-LAX with PHX as just a connection, the airline can cancel PHX-LAX and put you on a direct JFK-LAX flight and still meet their obligation. There's nothing you can really do about this if you really wanted to go to PHX.
However, a stopover is really just a long connection but since it's specifically part of the fare rules, it acts like a destination. For example, I've seen Cathay Pacific offers trans-pacific fares with a Stopover in Hong Kong that allows you to stay there for several days for the same fare as a connection.
But, if one flight is cancelled, you will probably have the option of going direct, or rescheduling to include the Stopover if you really want to go to Hong Kong.