In my limited experience at Purdue, based on our active parent group and what I heard from D, most change major and a small handful transfer.
There are 17 engineering majors at Purdue and only 4-5 are at capacity any given year (so far anyway). If students aren’t admitted to their first choice, they’ll pick a related second choice. For example, BME is often at capacity so students will do mechanical or straight biological engineering.
Usually the transfer stories are from students who were trying to transfer into CoS or CoE from exploratory studies or a different college, which is an uphill battle. Admissions is up front with students that if they have a CoE admit elsewhere, they should pursue that. Exploratory studies really shouldn’t be offered any more to students as a back up who want engineering. It’s no longer a viable pathway.
(My prediction is that will happen in the next few years and they will just start rejecting more applicants.)
Related, I heard more stories of students struggling with all the math and physics and transferring to polytechnic for more hands on/less math heavy majors.