The Scrum method advocates keeping two backlogs - a product backlog and a sprint backlog; the sprint backlog is created by the team off the product backlog at the beginning of a fixed duration sprint (and adjusted by the team if needed), and the sprint backlog belongs to the team, and can't be changed by the business / users (instead, new issues go to the product owner, who can add them to the product backlog for them to get picked up at future sprints). The team is supposed to produce something that is 'complete' for some definition of complete at the end of each sprint.
Because sprints are fixed in time (maximum of one month) and have finite scope (whatever items on the product backlog the team are able to take to completion), each sprint delivers iterative forward progress towards the long term full set of requirements, and even if the project runs out of money after a few sprints, the most important requirements will have been met. The product owner still gets to prioritise a backlog (the product backlog) according to business and user requirements.