Dealing with “blank” inputs in prediction of a neural network?

Say I'm training a neural net to compute the following function:

(color_of_clothing, body_height) -> gender


When using this network for prediction, I can obviously plug in a pair (c, b) to receive a predicted g, but say I want to get a prediction only based on c or only based on b, can I use the same neural net somehow? Or would I need to train two separate neural nets c -> g and b -> g previously?

Or more generally, can I use a neural net that was trained to predict A -> B to make predictions on values from a subset of A, or should I train separate neural nets on all subsets of A that I'm interested in?

I think the answer to your question would be "yes". Though inference would always be best if you provide representative training data. For example you can train your net with (c, b) pairs, (blank, b) pairs, and (c, blank) pairs. That would make the net more robust and likely to support your use case. Training separate nets for each case would be more efficient and accurate - but I'm not sure what your goals and constraints are.
The point is a "blank" input can be trained for as well in the same net. In your case it's a new kind of body_height or color_of_clothing. I also suspect you might have issues with how you encode blank because e.g. rgb(0, 0, 0) would be black, and perhaps you intended to model blank as zero which would mean a blank is black.