This happens when people confuse estimates with deadlines.
I've had clients trying to negotiate my estimate downwards. So stupid. Why would you want to underestimate the actual needed time? You want to go over budget?
They want to negotiate your estimate down, so they can then pin your quote and budget to the lowered estimate.
"Going over budget? That's fine, let's renegotiate. Remember though that you're already behind on this project so that needs to be taken into account. We'd prefer this last leg of the project to be flat rate..."
It's definitely not right - and as a contractor your should read the tarot cards and have had preparations in place so it wouldn't happen - but you'd be amazed at how often variations of this scheme work out with PMs and procurement at larger companies that should really know better.
I've had clients trying to negotiate my estimate downwards. So stupid. Why would you want to underestimate the actual needed time? You want to go over budget?