Bones Value -0

Yeah, it's exactly that floating point precision as Voxel mentioned. For example, try setting a float attribute to -0.0000005 . If the precision setting Voxel mentioned is set to anything less than the amount of numbers after the decimal point in that number you would see -0.

As for IK handles in particular, they need to make sure the ik chain is lying on the same plane, so the first time it evaluates it will need to adjust the joints rotations even if it's ever so slightly, but that could result in negative numbers which are so small, that are not covered by our precision setting.

Sounds like you're asking why sometimes the rotation values flip between 0 and -0 when you have constrained objects in general. If so, that's nothing to worry about - Maya calculates positions and stuff up to a certain decimal point, but the math isn't exactly perfect. it's probably just moving a little bit off from 0 in either direction. Channel Box --> Edit --> Settings --> Change Precision