What will happen if almost constant values for features?
If a feature is truly constant across all the instances, then it's useless for classification and it can be removed.
But in any other case, as in your example, a feature can be useful even if constant with most instances. In your example it might turn out that the target class is strongly correlated with type_of_residence, so it would be a mistake to get rid of it since your model can take advantage of it.
Unless you have a good reason to get rid of a feature (expert knowledge), keep all of them. If you must reduce the number of features (for instance to avoid overfitting), then the selection should be based on information about which features are the least informative (e.g. using some correlation measure).
Ideally the best way to know which features are useful is to try to train a classifier and evaluate it with every possible subset of features (but it's rarely possible in practice)