Dynamic languages will allow a range of types through functions. JITs add tracing and attempt to specialize the functions based on the observed types at runtime. It is possible that later on, the function is called with different types than what the JIT observed and compiled code for. To handle this, JITs will have stubs and guards. You check the observed type at runtime before calling the JITted code. If the type does not match, you would call a stub to generate the correct machine code, or you could just call into the interpreter slow path.
An example might be the plus operator. Many languages will allow integers, floats, strings and more on either side of the operator. The JIT likely will see mostly integers and optimize the functions call for integer math. If later you call the plus operator with two Point classes, then you would fall back to the interpreter.