。
The defector crossed the border safely.
Literal
Defector [topic-は] safely border [object-を] crossed
亡命者 is specifically a political refugee or defector — one fleeing their country, typically for political reasons. 無事に is the adverbial form of 無事, 'without incident / safely'. 越える (to cross over) rather than 渡る emphasizes going over an obstacle or boundary.