I suppose it could be something else but it is probably from a past tenant's dog.
With an old spot like that - large in size - you can try to soak the carpet..more importantly, the padding with NM or the like. Will probably take more than one attempt. Then, perhaps shampoo it all with a machine and NM in the solution.
If that doesn't work - and it may not - the only real answer is to replace the carpet and padding. I understand this is your landlord's job so hopefully you can convince him. Shoot! Show him the black light thing. From my past experience with landlords, though..that's going to be a tough sell. You might have to eat the cost and do it yourself if it means that much to you.
Sorry - I know that's not the answer you probably want to hear
