If you put a bodygyro on a Character and set the P value to Inf, the character will randomly have their positions and some orientations set to nan, as seen in this video:
With streaming enabled, the results cause roblox to stop responding:
Image of Character properties:
Image of Gyro properties:
BodyGyros (and all instances with the Body prefix) are deprecated. They are no longer updated to fix bugs, and you should instead use an AlignOrientation.
Why you gotta hurt me like that phoenix 
But on a serious note, Body physics objects can still achieve specific results that are impossible with the modern constraints, so until they’ve been completely replaced, they still have value.
Do you have any use case that couldn’t be covered by, or mostly by constraints?
True, but in the mean time, don’t set P to infinite. 
I’m going to have to second blueberry’s response. Looking at the code, we do have some safeguards in-place to scale input P and D but their purpose is mostly to ensure that these quantities are reasonable relative to one another. Everything starts breaking down once quantities head to infinity. Is there a particular behavior you are hoping to achieve by setting P to be infinite?
On a related note, can you elaborate on some of the results that you can’t currently achieve with the mover constraints? We have spent quite a bit of time recently trying to achieve parity between the deprecated body movers and the equivalent constraints. We would love to know what is still missing. Thanks.
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