If you put the tax low enough you either have to pump money into the city from elsewhere in the state/country, or you have to severely cut down on infrastructure maintenance, police, fire department, etc to cover the costs. Which would mean that you get increased crime and other issues, which would mean it becomes less interesting to live there or to start a business again. After all, if enough cuts affect the police and/or infrastructure it may take longer for cops to get to a crimescene.
If you pump in enough money at the same time you might be able to keep it up a while, but that money has to come from somewhere. It would then probably be wiser to put the tax rate at a decent level to match the rest of the state, and to give some temporary 'benefits' to people willing to move there or start a business. When the benefits then end (when the economy picks up) you don't need to raise the tax rate to cover future costs.
Of course, no matter which solution you go for, it does require pumping money into the city to try and save it. Which means that others will pay for it via their taxes.