Out-of-state renters - too good to be true?

[Yuri Chernousko]

For those who screen tenants on their own: does any of this feel like a trap?

- A prospective tenant replies via CL to my ad of a house.

- Says they (herself + husband of many years) are packing a car to move from a bank-owned house out of state and need a house to rent in my town.  The story is that they have been renters for 10 years, the landlord dies in debt, the bank is taking the place and relocating them, the tenants.  They chose my town because of its proximity to an ill friend.  They claim both to be self-employed in personal assistant/mechanic kind of work.

- They offer friends' and family's phone numbers as references; of course, only the best character references.

- Here: They say they can prepay 6-7 months rent.

So far, sounds like a messy but possible story.  No requests yet of my bank, paypal, etc. information, but they insist on the urgency of their situation.

Anything here looking like a pattern to avoid?

Thank you.

Yuri