Stuck MAP sensor

The MAP sensor is plastic and it's in the intake system, usually bolted to the side of the throttle body. If you're working in the exhaust system, you're working on an oxygen sensor. Those can become rather tight. I use a combination wrench with the box end on the sensor, then I hook another wrench onto the open end to get more leverage.

When they're really tight, I cut the wires off, then pop a six-point deep socket on it, and I use a really long-handled ratchet. Never had one that wouldn't come loose that way.

You might get more ideas from this article too:

https://www.2carpros.com/articles/how-to-replace-an-oxygen-sensor

You said it's in the exhaust manifold, hence the confusion. There is sealant on the threads, but I've never had one break. If the engine runs, consider warming it up to let the plastic soften a little, then try to unscrew it. Slow, steady pressure is more likely to break it loose than a sudden hard twist.

If I had one break, what I would do first is heat the remaining threaded part up with a hot air gun, then use a broken bolt extractor to grab the piece and try to turn it. There's at least three different types of bolt extractors. The most common style might get the job done, but it is going to expand the part more as it is screwed in further. That's the style shown in the top of the photo. The type I prefer is shown in the lower part of the photo. The blue arrow is pointing to one size in the set. It's a straight metal stick with grooves cut into it. You tap the right one in and it cuts matching grooves. This will go into plastic very easily, but if the plastic is that brittle that it broke, this tool might just cause it to crumble even more.

Once the shaft is tapped in, you use one of the collars, (light green arrow), to turn it with a wrench or socket. This set can be harder to find. If you have to resort to this drastic measure, start by looking for the set at an auto parts store that rents or borrows tools. In my city they make you buy the tool, then you get a full refund when you take it back. If you choose to keep a tool, you still take it back, then they give you or order you a brand new one.

You can also visit any repair shop and ask when the guys who drive the tool trucks show up there. Typically that's once a week, but any mechanic can give you their phone numbers, then you can find out where they are going to be at a specific time and day. Those guys will usually have a few different sets on the truck.

Please keep me updated on your progress, or if you have more questions.

What type of problem or symptom are you trying to solve?