Yes its common... dogs will do the same, if they lose a long-term life-companion. It can give rise to what I guess you can call psychological disorders that will manifest in physical symptoms... my mate had two cockers and one had to be destroyed, - - the other went from being a very amiable, 'normal' dog to being a nervous wreck that couldn't be left on its own, or it would sh*t and spew all over the house, it wouldn't eat for days and days at a time, much of its hair fell out... all diagnosed by the vet as a mental / nervous / pyschological disorder.
Cats can, and do , exhibit very similar behaviours.
The vet advised my mate to try and alter the animal's normal routine as much as possible, to help alleviate the symptoms. Change in diet can definately form part of this change.
You could try 'reversing' its in/out time... if it was habitually put out at night, and in during the day.. swap this over... its a lot to do with changing its stimuli and for want of a better way of saying it.. " challenging its perceptions of what it considers to be the norm", if that makes sense.
Hope the puss comes OK...
all the best,
Aj.