How to make an Animator NOT set the default value of a property that's not animated right now?

I have a property that is, 90% of the time, modified by scripts. However, in one and only one animation, I have animated the property.

The issue is that, because ONE animation in an Animator controls that property, the Animator now overrides that property to its "default value" when that one animation is not being played. This behavior makes sense in a lot of cases, but is there a way to disable the behavior when it doesn't?