I have an undesirable unit which is not renting.

The poor are largely ostracized because they are in need and they live in undesireable neighborhoods.

Also, a simple google maps street view will show you if a property is undesirably close to a freeway, etc, which would save you a trip to a property you likely will not have interest in.

Amanda Han (CPA) touches on this peripherally in the last podcast.  

In other words, in New York, an applicant for an apartment can tell you that he or she is planning to live in the apartment by his or herself, go through and clear your background check, move in, and then permit another person with a criminal record (or any other undesirable rental history characteristic) to move in. 

As many people have implied, only law-abiding citizens will heed your ban on firearms, and the armed undesirables will ignore it and keep their guns.  

I know I can FHA the property, but the good deals would force me and my wife to move to the straight up undesirable areas.

Low demand/undesirable areas=low prices.

I’ve always heard to stay away from these types of properties, because they are undesirable to tenants.

Folks in CA like to say that their overall population is not affected and/or that the people leaving are just poor, undesirable.