How can I tie a coroutine's lifetime to the lifetime of an object?

I have some code similar to this:

class Foo {
    var x = 0
    
    init {
         GlobalScope.launch {
             while (true) {
                 delay(1000)
                 x += 1
             }
         }
    }
}

How can I ensure that the coroutine will be cancelled when its owning instance of Foo is garbage collected?

You can't, certainly not with the code as architected. You must in general manage the lifetimes of coroutines -- and their scopes, strictly avoiding the use of GlobalScope -- more explicitly, e.g. making your Foo a Closeable and managing an explicit CoroutineScope associated with it that gets cancelled when the Foo is closed.

Even given the limited ways to take action on the garbage collection of a given object or reference, the structure you've specified permanently retains a reference to Foo for the lifetime of the coroutine, so it can never be garbage collected.