Comment by immibis

Another reason Java applets ultimately failed was the never-ending stream of sandbox escapes, which is inherent to their design of running trusted and untrusted code in the same VM and trying to keep track of which is which. It turns out it's much more straightforward to sandbox the whole VM.

A representative vulnerability is "trusted method chaining". You (the attacker) construct a chain of standard library objects that call each other in unexpected ways. You can make use of the fact that you can subclass a standard library class and implement a standard library interface, in order to implement the interface methods with the base class's implementations, to construct more unusual pathways. Then you get some standard library entry point to call the first method in the chain. Since your code doesn't appear on the call stack at any point (it's just the standard library calling the standard library) whatever is at the bottom of the call stack, at the end of the chain, infers a trusted context and can access files or whatever. Of course, finding a method chain that's possible to construct and does something malicious is non-trivial.