The corp's id is the New Angeles Sol: Your News and some current is on the table.
Say runner steals an agenda. What is the order of abilities triggered? The current is trashed and then corp's id can bring it back, or not?
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New Angeles Sol: Your News allows you to play a current from HQ or Archives (paying its play cost), it does not prevent anything from happening.
After an agenda is scored or stolen, this ability triggers at which point you can play any current that is in Archives (or HQ). If a current was trashed as a part of scoring or stealing the agenda then the current will be in Archives and available to play.
This isn't quite the same as 'preventing' trashing, or making currents untrashable as they still need to be played and paid for.