If you have a legitimate reason (or at least tell them you did) then it should not be a problem. If you did not pay the balance on the contract, it is remotely possible that your previous company would give you a less-than-stellar recomendation but most companies would be too afraid of getting sued to even go that far.

If anyone asks you about paying the contract, just say that you are having hard times due to the aforementioned family emergency and will work out a payment schedule when you can.