System Information
Operating system: Kubuntu 18.04
Graphics card: GTX1080Ti / GTX690

Blender Version
Broken: 2.80, 957b4547aeeb, blender2.8, 2018-12-28, as found on the splash screen
Worked: 2.79

Short description of error
Drivers that reference custom properties do not update correctly.
If the custom property value is smaller than 1, it updates the driver to 0.
If the custom property value is bigger or equal to 1, it updates the driver to 1.
Problem remains with object-custom properties and armature-custom properties.
Works correctly with non-custom-property-variables.

Exact steps for others to reproduce the error
Open a new blender file.
Create a custom property on the Default Cube Object. Increase its hard limits.
Make a driver for X location. Use single property for variable and reference the custom property by path.
Slide the custom property. X only updates to x=0 or x=1
Try in 2.79. X updates exacty to the value of the custom property.