The most popular scam by far to pull on a landlord is by posing as the landlord. This is most often used when the landlord lives off the premises. A person will pose as a tenant and get a lease for a certain price and it will seem as if everything is perfectly fine. This person, however, will then turn around and pretend to be the landlord to the same place and rent out the apartment at a higher price. This means that not only are they earning money on something that isn't yours, they normally don't screen anyone and take whoever they can get at that price. This means that there is someone in your rental property who you do not know and there may be little that you can do about it.
Having a fully fleshed out lease is one of the most important things in a situation like this. Often, landlords will have a specific clause in the lease which states that no one else may live in the apartment without prior approval. Having this written in is actually extremely valuable in a situation where a tenant is trying to scam you. If this is written in, then you can find someone in direct violation of the lease and beginning evicting measures is much easier.
We always suggest having someone in the area keep an eye on your property if you are not nearby. This isn't foolproof of course, but if someone sees something that can be suspicious they can easily give you a call or send you a message to let you know. We need to look out for each other and this is just another way to do so. When all else fails, always trust your instincts if something doesn't feel right.