Giving your cats only tuna made for humans is a bad idea because of two things, firstly the high mercury content can give the cats mercury poisoning over time, and secondly the lack of taurine means you will actually be damaging your cat, by not giving it the nutrients its body needs. Cats cannot make their own taurine and require it, all cat food must contain it.
When my cat was sick, we bought him Carlyle's Just tuna for Cats. This was different tuna from human grade, it was the dark meat, and so was not in brine or oil, and had less mercury than other tuna. It also had nutrients added to make it for cats, including Taurine. We fed this exclusively to my cat for about 2 months until his stomach settled. It was the only thing that would spark is appetite, it has a very strong tuna smell and as soon as I opened the can he got exciteed!
We got his weight back up using this, and once he was healthy we switched back to a regular balanced cat food and haven't looked back!
Carlyle's is only around 70c a can, and cats love it! I totally recommend this Tuna only cat food option for anyone who has problems with a cat who has an upset stomach, or wont eat. Tuna is like crack for cats they cannot resist it, so it is a cheap, safe and easy way to get a sick cat to eat, and get their weight up whilst you work out a long term food / healthcare plan.
