I have a very dear friend who like most women here used to wear her pump in the Bra.
A small head on accident caused the seatbelt to push the pump violently into chest and cracked sternum, pump survived.
She only wears pump clipped to waist these days.
On a similar note carrying pens in breast pockets is a severe risk in accidents, another friend who is a nurse in A&E told of many people with objects such as pens/pencils pushed into chest who may well have survived otherwise.