although I'd expect there will be some minimum annual sales volume requirements to determine who needs to comply.
In New York, here are the choices for filing:
1. zero sales (not zero taxable, zero total) requires a return, although you can apply to file annually (instead of quarterly)
2. if you have discontinued the business, your return says so

The reason for the residence state and County (New York has 62 Counties and even more jurisdictions - some cities are separate also, which you must identify in your return) getting the money is simple: that's where the local vendors didn't collect the tax on a walk-in sale.