Developers of anything resembling complex scripts (for the time) had to manually break these cycles by setting to null the attributes of the DOM node that had references to any JS objects.
Douglas Crockford has a little writeup here[0] with a heavy-handed solution, but it was better than doing it by hand if you were worried another developer would come along and add something and forget to remove it.
Other memory managed languages also have to deal with the occasional sharp corners. Most of the time, this can be avoided by knowing to clean up resources properly, but some are easier to fall for than others.
Oracle has a write up on hunting Java memory leaks [1] Microsoft has a similar, but less detailed article here[2]
Of course, sometimes a "leak" is really a feature. One notorious example is variable shadowing in the bad old days of JS prior to the advent of strict mode. I forget the name of the company, but someone's launch was ruined because a variable referencing a shopping cart wasn't declared with `var` and was treated as a global variable, causing concurrent viewers to accidentally get other user's shopping cart data as node runs in a single main thread, and concurrency was handled only by node's event loop.
[0] https://www.crockford.com/javascript/memory/leak.html
[1] https://docs.oracle.com/en/java/javase/17/troubleshoot/troub...
[2] https://learn.microsoft.com/en-us/dotnet/core/diagnostics/de...
