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If I have a settlement with many roads connected, let’s say at least 6 roads deep, and my opponent cuts it off and builds a settlement between them, can I still build a settlement at the deep end even though my roads aren’t connected to my settlement anymore?
You may only build a settlement at an intersection if all 3 of the
adjacent intersections are vacant.
Each of your settles must connect to at least one of your roads.
If you don't break either of those rules and you have the resources you may build a settlement.
You might be getting confused with how a player 'breaking' a road with their settlement can shorten the longest road. Another player building a settlement on your road doesn't prevent you building a settlement if it is not adjacent to where you want to build.