stampede in(to some place)
[for a crowd of people or other creatures] to move rapidly into a place, as if in panic. The shoppers stampeded into the store the minute the doors opened. The doors opened and the shoppers stampeded in.
stampede out of
some place [for a crowd of people or other creatures] to move rapidly out of a place, as if in panic. The patrons stampeded out of the smoky theater. The cattle stampeded out of the corral.
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.