Broken Dipstick 2010 Corolla

#1
My 2010 Corolla has a broken dipstick, the dealership just found it when I was getting the oil changed, the oil had last been changed 4000 miles before this past August. I never check the oil because I get it changed regularly. I have no idea how this might have happened. They say it will cost $390 to replace because they have to take off an air-something (I'm car illiterate) and then replace it just to get to the dipstick.

Question: How essential is this? (Can I wait a month, months, etc.?)
Is their charge reasonable?
How the heck could this have happened?

Any help would be gladly appreciated, thank you!
 
#2
Air-something does not makes sense. all they would have to do is remove the oil pan and it would likely just fall out. I would not drive around with a piece of metal like that in the oil. Did the dealer just give it back to you to drive away?
 
#3
Air-something does not makes sense. all they would have to do is remove the oil pan and it would likely just fall out. I would not drive around with a piece of metal like that in the oil. Did the dealer just give it back to you to drive away?
Thanks for the reply. It's the intake that they'd have to remove. I apologize for getting that wrong. My understanding is that it's situated around the dipstick (above the o rings) and that for them to get to the dipstick they'd have to remove it and replace it. And that that's the main reason for the high cost of the procedure ($390 was the quote, though there may be some kind of discount).
 
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