The only way you could get such behaviour would be to replace the current reference with a view based object such as detail line perhaps. The other option is to create some kind of faux dimension via detail component family that looks like a dimension but isn't one. This can be high risk strategy and goes against Revit methodology (having a potentially incorrect dimensional value).
Having said that sometimes dimensions disappear due to small changes and their omission completely change what is represented. probably should adopt an overall strategy of comparing last revision against new revision.
