It was not only the bounty placed on the Tasmanian Tiger that led to its extinction, rather it was a combination of things that ultimately killed them off. These things were the introduction of dogs creating competition for food, a disease spreading and killing the Tasmanian tigers, the loss of habitat caused by humans, and of course the bounty placed on the Tasmanian Tigers. The species may have been able to keep on living if it were only maybe one or two of these things, but when it was all added up it ultimately led to the demise of the species.
Also, even if there are still Tasmanian Tigers out there, there are not many of them and they are most likely closely related. So, even if by the slim chance they found each other and bred, they would probably give birth to an inbred baby. So, the survival of this species, even if there are some alive, is extremely low especially if you factor in that to avoid getting shut down, lumber companies in the area will try to kill them off if they are ever found or sighted.
There has also been attempts made to try and clone this species to try and undo the damage humans have caused the Tasmanian Tiger but the DNA they had collected was not good enough to successfully clone them with our technology. Maybe someday it will be, but it isn't quite yet.