0: https://arxiv.org/abs/1802.05300
1: https://en.m.wikipedia.org/wiki/Errors-in-variables_models
The thing is that some of the techniques commonly applied when training NN are often "good enough" to deal with the presence of corrupted data (e.g. using SGD to optimize a model, while applying weight decay and drop-out, adds a regularization effect that somewhat replicates the effect of assuming errors-in-variables), as long as the input data is not total trash, which deters people from applying more formalized robust approaches to it.
As long as "things kind of work", it is difficult to convince other people to adopt robust methods, particularly due to the existence of a "robustness vs. efficiency" trade-off (which can make robust methods seem additionally "unsexy").
i.e. if the majority of data fed to a system is bad, will it work?
Outlier detection detects data points that look different from your existing data in some way; that "lie outside" what is usual. Sometimes the assumption is that outliers are generated by an entirely different process from the rest of the data. It's important not to conflate "outliers" with legitimate data points that happened to fall at the tail ends of the data distribution.
The techniques I listed attempt to actually compensate for some known or estimable level of badness in the data. For example, gold loss correction (GLC) essentially estimates the probability of misclassifying a data point, and uses that to adjust the output of the model.