When braking the car pulls to the left

Something is shifting between cruising and braking that allows the alignment to change. Worn ball joints and tie rod ends are common suspects. If one of them separates, you'll lose control as the car skids into the ditch or oncoming traffic.

Worn control arm bushings are also somewhat common. While they will let the alignment change, they aren't exactly a safety hazard. You'll have reduced steering control and handling, but no sudden catastrophic failure.

The people at any tire and alignment shop will be able to figure out what is causing this problem. Have the car inspected right away, and any time you feel a vibration or hear a clunk or other noise.

Here's a link to an article that might provide more information:

https://www.2carpros.com/articles/car-pulls-right-or-left-when-driving-or-braking