Our lease specifies that the tenant pays until the new tenant starts their lease - and specifies that they will pay all advertising fees. I agree with sol regarding credit scores. The ONLY challenging tenant I've had was when I decided to relax the credit score requirement a bit because my former tenants would rent for a year and then move out to buy a place of their own. I was hoping that tenants whose credit was not stellar would stay longer. It backfired and I got into a 2 year lease with the tenants from hell. Fortunately, they broke the lease early and we were happy to see them go.
After that experience, I will never believe another reference. Their former landlord gave them a glowing reference to get them to leave his property and move on to ours.
Out of curiosity, why did you ever in the first place? Ever since about age 20 when employers started asking for references, I was just overwhelmed by the pointless futility of it. Why would someone completely discount what they think about a person whom they've had the chance to talk to and evaluate for an hour or so, at the opinion of a stranger who you don't know, has zero obligation to you, and will never hear from again? Truly if someone provides references, the only thing you can be sure of is that they have friends.
Obviously if you have mutual acquaintances with a duty of care to both of you, the situation is different, but by and large that's the exception.
Perhaps it's just a way to avoid responsibility on the part of the property management/HR? If things go south "well I did everything I reasonably could, checked references, so it's not my fault"?
And like you found out, people are very self interested. Their hierarchy of obligations goes something like myself-> my friends -> some stranger. So a great tenant will likely be called a bad one if it means some landlord can hold on to them, or failing that a friend will happily lie to advance their friends cause at the expense of some stranger they'll never see again (ie you), so once again I just don't get the point of references.