In English, a bear hug is a good thing, at least for people who like nice warm embraces. But in Hebrew, חיבוק דוב more often refers to a hug that is affectionate to the point that it becomes too much.
For example:
היא כל כך מגוננת עליו, שזה הפך לחיבוק דוב חונק.
She’s so protective of him, it’s become a suffocating bear hug.
Israel and the United States have a very positive relationship indeed. Despite that, you’ll sometimes see Israeli media portraying US influence on Israel and its policies as חיבוק דוב, suggesting that Israel loses some of its autonomy in the process of receiving so much support.
The word חיבוק is a noun form of the פיעל verb לחבק – to hug, to embrace.
