What would dynamically-typed languages actually do if type enforcement was removed? I program in Python, which is a well-known dynamically typed language. I understand dynamic typing to mean mainly that "operations" (in a loose sense) in the language are either allowed or denied (raise an exception) based on the type of their operands, and that this type-checking is deferred as long as possible. My question is this: if that is what a fair characterization of dynamic languages, what would happen if the run-time type checking was removed?

It seems to me that if you want to make a meaningful distinction between a dynamically typed language like Python and an untyped language, you would have to define what actually would happen in the untyped language in situations in which the type system of a dynamic language would take action. For example, in Python, if I attempt to subtract an Integer from a String, e.g., "spam" - 5, I receive a TypeError. If that's what makes Python dynamically typed, what would an "untyped Python" do in that situation?
A language in which automatic type checking is not available, an operation would make assumptions about the types of its operands. On the event that these assumptions are false, the operation, not knowing anything about this, may produce nonsense results.

Assembly is such language. It has, for instance, separate addition operations for integers and floats. If you perform integer addition on floating point values you will get a result which is correct as neither integer nor float. Depending on your definition of correct.