stampede into (some place)
1. To rush into some place all at once and in, or as if in, a wild panic. A great mass of people stampeded into the department store at the crack of dawn to avail of their Black Friday sales. The herd of cattle, spooked by the loud explosion, stampeded right into the gorge to their deaths.
2. To enter into some place in very large numbers. Following the second World War, people from all over the world began stampeding into the country in the search of better opportunities. Would-be prospectors stampeded into the region in the search for gold.
stampede someone or something into something
to cause people or other creatures to move rapidly into a place, in panic or as if in panic. The loud noises stampeded the crowd into the parking lot across from the stadium. The cowboys stampeded the cattle into the corral.