Deadlines are always negotiable. It's taken me so long to realize that people just want to know you're on top of something. Simply saying "This was deprioritized this week/month/quarter in favor of other work, but I'm still on top of it" buys you a lot of trust. My inclination is to deliver either good news or no news at all – I have to work to fight this.
If you already have trust from those who enforce the deadlines. As you point out, a deadline is an accountability mechanism. But if you're otherwise accountable and trustworthy, the deadline isn't really the metric that matters (most of the time).