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or watched extra rent vanish by movingOh let me list all the ways a landlord will screw you!
It depends, heavily, on lease agreement. Where I was, a lease is for a given period of time, often 12 months. (Not aligned to anything: literally $DATE_WE_SIGNED to that +12 mo.) Breaking the lease requires paying it to completion. On average, that means 6 months of rent. Now, if you did the work of finding a tenant that the landlord approved of, that new tenant could then take the apartment (and you'd be off the hook once they started renting).
Since I know many people think this: leases don't necessarily turn into month-to-months: legally, they could, but my landlord typically did not allow this to happen: at the end of the 12 month lease, they will typically raise the rent at which point the lease contract gets renewed: often you have two choices: renew for 12 months at the higher rent, or renew as a month-to-month at an even higher rent; IME, around 5%. Now you have to balance the likelihood of moving vs not: if you don't move, you'll pay 60% of a month's rent over the term of the lease for nothing. Even if you are moving, you might not be moving at your lease date exactly, so even with planning, if you degrade the lease to a month-to-month on the renewal prior to your move, there might be a few months were you're paying 5% more just 'cause.
Giving notice to quit usually requires, e.g., 30 days, so you'll be on the hook for next month's rent, too, even if you'll have moved out by then. This is hard to avoid, since otherwise you risk not having a home if you can't get the next play lined up.
Now, of course, if you're going to move, and you can plan, at all, then you do everything in your power to align these stars to minimize the cost, doing whatever is appropriate for whatever state your lease is in.
(In my case, we opted to turn the lease into a month-to-month, and paid exactly 2 months at the higher rate, or ~10% or $200 over the 12 month. That renewal weirdly also came with a 15 mo option, which was new; over that rate it cost $300 to abandon ship. Honestly, other factors dominated, like pay adjustments due to new locale, local housing costs, even just the moving costs. But it did occupy time, worry, and made logistics unnecessarily more difficult. We also had no overlap due to the magic of family and the nature of our move.)