Is it possible to lose a city?

As @Chippies said, no, there's nothing you can really do once your account is negative with a negative cashflow. Its not direct, but it is a way of forcing you to abandon the city.

You are technically going bankrupt when you go into negative cashflow. After that you need to decide whether or not you want the effort of saving the city. From personal experience of someone who managed to get out of debt, it's easier to abandon the city. It took me a few hours to get myself out of debt.

HOWEVER, if you're attached to the city and want to get out of debt no matter what, you need to be able to give the people what they want, hence why I build roads unzoned. If you can't do that, then trash the city and start over.

When I build my city, I intentionally build plenty of roads, but don't zone them yet. The roads are the only thing I build in excess. I tested whether or not I could actually get out of debt of negative 10 million with negative cash flow of 300K.

I managed to pull it off but it was hard as hell.

1) As you go into debt, you will no longer be able to build and people will begin to abandon the city. Make sure you demolish those buildings ASAP. Otherwise you'll be spending ages demolishing houses. Also, make sure you don't accidentally demolish a road.

2) Watch the demand bars, if your people want Industrial, and your only free roads are next to residential, don't worry about pollution right now, you're more concerned with upping your population. As your population increases, your income increases and your negative cash flow will slowly move towards positive.

3) Shoot your taxes up to 29% periodically, but not like crazy, or you'll piss off the people and they'll STILL abandon the city.

4) Since you're demolishing abandoned buildings you're also destroying your power grid. If you demolish a very large area, then you might as well dezone that entire area, and rezone it so that you have control over where people move in. That way all the buildings are connected and you still have a power grid. If you don't have a working power grid, your people will STILL abandon their houses.

5) This is dependent on how big your city was when you went into debt. If you managed to reach the Big Town milestone, and have access to High Density Residential/Commercial, then it would be beneficial to replace the Low-Density with High-Density in the event that you went into debt since you get a larger population.

I got to over negative 3,000,000 dollars but it just keeps telling me to take a loan, putting me further into debt. So if you get below negative 100,000 start over there is no hope.