Wiggle position expression: How to stop and freeze?

Aside from what Andrew said, you may want to read this:

http://www.motionscript.com/articles/speed-control.html

You will run into exactly this issue. You may be able to animate the amplitude, but will lose any actual position info and using an integration expression will be pretty much unavoidable.

Mylenium

Your screenshot reveals nothing about your expression or what you're animating, but it's probably not important to answer your question.

Add an Expression Slider Control to your layer, then link it to either the frequency or magnitude of your wiggle expression.  In my example below, the slider controls the frequency of the wiggle.  Then just keyframe the slider to set the amount you wish to apply.  Obviously a value of 0 will mean no wiggle at all.