Had my passenger side front glass replaced yesterday. Landlord was cutting the grass and a rock busted the window. Yes, the landlord is paying for it.

After Safelite took the panel off he saw this piece sitting down in the door. He said it is the regulator but I don't see a motor attached to it. Is this the regulator?

 

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The motor is in the rear of the door. Just look a bit you will see it. It's cable drive so there are several cables running around in there too. A flashlight will help.

Check for small bits of broken white plastic in the bottom of your door. That's from the regulator starting to break. Now would be a great time to change it if needed.

Sorry about having the picture above! Just wanted to label it to make sure I understood what you were pointing to.

Also vacuum out the inside of the door to get all the broken glass out. The first six months I had my car I could hear noise inside my drivers door. Finally took off the door panel and found a bunch of broken glass in the bottom of the door. Looks like the car was broken into or accidentally broken like yours. The glass shop for sure won't worry about it!
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Looking at your picture it is the metal part on the left that the rubber is attached too that broke off.

 

That part holds the glass. It has a bolt that goes through it to pinch the window. If the bolt is out of it then it just needs to be put back in. If there are plastic pieces attached to the metal part then that piece of the regulator broke off and the regulator would require replacement.

 

Yeah the white plastic piece was still attached to the metal.

 

I did not realize that the Safelite Tech left the piece in the car. Do I have to replace the whole regulator or just this piece?

 

You will need the whole regulator. I don't believe that piece is even sold separately as it is basically impossible to get on/off without breaking (I don't believe it is designed to come apart).