Note that there's not much left to mine on testnet: the block reward is now 0.024, about 300 times lower than Bitcoin mainnet.
For that reason, it is very unlikely that testnet3 will ever be killed. Because now, it is the only network that is quite close to mainnet, and where you can test, what will happen when the basic block reward will be very small. It is also probably the first network, that will reach zero block reward, and then a lot of people will carefully observe, what will happen next.
By the way, testnet coins are worthless by definition. So, if nothing else will happen, then testnet3 will finally reach a state, where the basic block reward will truly represent the real value of those coins. In general, testnet3 could have zero supply, but some coins are needed as a spam protection.
It's worthless already, and yet, people are mining it. So I expect at least some of them to continue mining when there's no block reward left. That also means total fees can be under the dust limit.
Testnet coins already seem to be quite scarce, my guess is many are lost. After all, there's not much of a reason to be careful with worthless coins. That means testing in the future will have to happen with smaller and smaller amounts.