That is a question that I shall answer in this essay, based on personal beliefs and what I've seen from my time on places on the web that I REALLY shouldn't have been (the transformation webring, anyone?) but usually, they are still conscious, if the author doesn't give up when it comes to writing the mind of an inanimate object. Panpsychism isn't for everyone, but it sure as hell helps when you need to write what happens. I find it very hard for me to enjoy inanimate transformations if I do not know what happens to the victim's mind.
Surprisingly, loss of consciousness altogether isn't very common. Usually it's no changes (which makes me even more sad than not being told what's going on in their mind, opposite most people who prefer them keeping their mind, but to me, I find mental changes after being turned into an inanimate object comforting), but the changes that do occur include obedience to the person who owns the object, obsession with what the object does, or embarrassment SO BAD it erases the rest of their mind.
For example of the second, I wrote a short story about a doll named Misty: Misty was once a person, but she was somehow turned into a doll, and for a few moments, the person-turned doll was horrified, until she began to forget ever being anything but a doll, and soon her mind began to desire only one thing: to be played with. Without the mental changes, I would've felt so depressed and scared for Misty. I still do, but I feel calmed down knowing she can no longer remember being anything but a doll. A doll was chosen because those are an inanimate object that comfort me slightly more when a person is transformed into them, because if someone is turned into an inanimate object that looks somewhat human (or has a face) it feels a little more comforting for me
A dramatic drop in intelligence may also be expected with the package of identity changes. Maybe not dramatic per say, but I've seen my fair share of people turn into an object that could only refer to itself in third person (Can't see...can't hear...toy doesn't need to...toy doesn't deserve to...). If they ever somehow get turned back to normal after the dramatic intelligence drop, I'd pray to god they had a brain surgeon and a rehab coach on the line to welcome them back to humanity. *giggle*
Back to the point:Although mentioning this may seem futile, usually, the object is filled with pleasure at what they've become and what they're doing, usually orgasmic (but not always). If Misty the doll gets played with, she feels a large amount of joy which is multiplied when the doll gets to interact with another doll, or the doll is put into a playset. This is to be expected, as if they still remember their past, the pleasure makes them enjoy doing their purpose more and more.
In rare cases, the inanimate object can talk. This isn't too common, as it makes them seem more animate than they should be, but in most cases, this will require less mental changes, unless the object does not become an annoying asshole constantly talking about how much it needs to be used, which it may or may not become. Misty can not talk, so no funny anecdote about her here, sadly
A thing I would like to see is the friends family, and other such people reacting to the transformation of a loved one. For example, a missing person report could be put up for the person Misty the Doll used to be, or her family could react to the disappearance
Basically: When someone becomes an inanimate object, they stay conscious, but their mind gets changed up a little bit
Posted on some encyclopedia dramatica ripoff circa late 2008, by me