How can I use an $n$-input neural network to predict some values for $n-1$ inputs? I have a fully-connected neural network whose input is a vector of $n$ (normalized) integers. Each of these integers is associated with an object. The output is similarly a vector of $n$ values each of which is the prediction of a metric corresponding to one of those objects. The network is trained using the data of all $n$ objects.
Now, I need to consider the prediction scenario above in a faulty manner, say, a fault just eliminates one of those objects. Now, I am wondering whether or not I can use the very neural network above to predict the features of the remaining $n-1$ objects. In particular, I don't who what I need to feed into the input associated with the eliminated object.
Any thoughts and ideas are welcome!

You could have an additional $n$ binary inputs which indicates whether each object is present or not.
Alternatively, you could have an architecture which can take in a variable number of inputs and produce a variable number of outputs. For example, given inputs $x_i$, embed them to $z_i = f(x_i)$, then let $z = \sum_i z_i$, and have output $y_i = g(x_i, z)$, where $f$ and $g$ are both neural networks. This scheme doesn't rely on there being any fixed number of objects.
