The new write-up from OP is that you can "forget" a future (or just hold onto it longer than you meant to), in which case the code in the async function stops running but the destructors are NOT executed.
Both of these behaviors are allowed by Rust's fairly narrow definition of "safety" (which allows memory leaks, deadlocks, infinite loops, and, obviously, logic bugs), but I can see why you'd be disappointed if you bought into the broader philosophy of Rust making it easier to write correct software. Even the Rust team themselves aren't immune -- see the "leakpocalypse" from before 1.0.