Hallman (2013) discusses some apparently contradictory data involving English do so. The received view is that do so is incompatible with the passive (Hallman's example 5d):(1) *These books were left in the classroom, and this cell phone was done so, too.
The typical account of this is that do so is a pro-form and does not have internal structure that can support extraction. The passive subject must move from an object position, but with do so there is no such position. What is surprising and apparently contradictory is that unaccusatives, which are also thought to involve movement from an object position, are compatible with do so (these are Hallman's examples 50a-b):(2) The river froze solid, and the pond did so, too.
(3) The towels dripped dry, and the socks did so, too.
Unaccusatives pattern with passives in many ways, which has led to the hypothesis that the surface subject of an unaccusative, like the surface subject of a passive, starts out as an object. The fact that do so is compatible with unaccusatives but not passives seems to be problematic for this view.
However, it appears from a web search that do so is in fact compatible with passives, at least for many speakers. The following are some examples found on the web, which do not seem to me to be ungrammatical (though some are a little awkward):(4) This means that the only the most edible meat is eaten and done so with much chewing as to liquify the food. (http://www.ehow.com/about_4740227_scorpions.html)
(5) For those who do not know Devil Fruits are extremely rare to find and the ones that are found and eaten are done so in mere happenstance unless you know what to look for. (http://shannaro.wordpress.com/2012/11/30/)
(6) I then take notice and observe when the food is brought to table that the meal is picked apart and what is eaten is done so in a controlled and seemingly not pleasurable manner. (http://www.psychologytoday.com/blog/when-food-is-family/201208/reflections-the-2012-olympics)
(7) Every photo taken and every update written is done so with the adoptive parents in mind. (http://godslittlestangelsinhaiti.org/andlifegoeson/2013/07/19/words-of-encouragement-adds-sunshine-to-our-day/)
(8) It is thrillingly written, and done so with the clarity and poignancy of a man who waited 62 years to reveal the full account of his experience, after first being approached by American prosecutors in 1947. (http://theboar.org/2013/04/19/denis-avey-believe-or-not-believe/#.UfJfWRz-nn0)
(9) And I think everyone can agree that some of the most beautiful music ever written was done so in the name of God or gods. (quote attributed to Anand Wilder, http://en.wikipedia.org/wiki/Yeasayer)
(10) The first ``Rosicrucian'' writings, the Fama Fraternitatis, Confessio Fraternitatis and the Chemical Wedding of Christian Rosenkreuz, all when written were done so anonymously and then later traced to be the works of Johannes Valentin Andreae,... (Tobias Churton, http://www.bonisteelml.org/invisible_history_of_rosicrucians.pdf)
From these examples it appears that do so is in fact compatible with any sort of VP: active transitive, unaccusative, passive, and so on. A simple account is that do so is a pro-form for a predicate that takes a subject. The actual predicate is retrieved from context and predicated of the surface subject of do so. This predicate can be a passive or unaccusative one, such that its subject will correspond to an underlying object. For instance, in example (8), done so is replaced with the predicate Lambda x.Exists y. x is written by y.
At the same time, the predicate can only be a predicate with an open subject (a one-place predicate), and no other open positions, so that extraction of other elements is impossible:(10) *I know which book Mary read, and which book Bill didn't do so. (Hallman 2013, (5a))
As in the traditional account, the predicate has no internal structure in the syntax, and so cannot support a gap. The only gap that is possible is the subject of the predicate itself.
The fact that do so is in fact compatible with passives renders Hallman's conclusions unwarranted and his theory unnecessary. There is no reason to think that passives and unaccusatives do not involve movement in the general case.References
Hallman, Peter (2013), Predication and Movement in Passive. Lingua 125: 76--94.