We could say that objects in the world do exist; they have objective properties like colours, shapes, sounds, tastes, etc. that (by any reasonable definition) are real. But their realness occurs only by virtue of the activity of a certain kind of mental apparatus, and this activity cannot be disentangled from the realness that the objects have. This on the grounds that if the operation of the mental activity is altered (through intoxication, through training, by surgery or lesion to the brain, as examples) the nature of the reality experienced can vary from the norm.
To answer the question, then, does an object x exist when we cease to pay attention to it (either by perception or conception) we can say that it does not, on the grounds that the quality of realness that any particular object has consists in part of the mental activity in play when the realness is experienced. Without that mental activity the realness, as such, is not in play. When we experience realness it is, quite literally, an experience, which is to say the experiental aspect is central to the condition.
