How to train a neural network for high recall?
There is a very simple way of increasing the recall of a network without requiring retraining:

A network's output is the probability it gives that a sample belongs to a class, let's say class $0$ or class $1$. The output of the net would look like this $(0.53, 0.47)$. This means that the net gives a $53\%$ probability of the sample being class $0$ and a $47\%$ probability of it being class $1$. Normally we check which class has the highest probability and consider that to be the network's prediction. However, you could set a threshold over which the sample would be considered to be class $1$.

This way you would get more samples predicted to class $1$, which would increase the class' recall (at the cost of its precision though).