diff --git a/src/isolate/connections/grpc/agent.py b/src/isolate/connections/grpc/agent.py
index 4dd0149..dd42e90 100644
--- a/src/isolate/connections/grpc/agent.py
+++ b/src/isolate/connections/grpc/agent.py
@@ -100,23 +100,28 @@ def execute_function(
         extra_args: Iterable[Any] = (),
     ) -> Generator[definitions.PartialRunResult, None, Any]:
         if function.was_it_raised:
-            raise AbortException(
-                f"The {function_kind} function must be callable, not a raised exception."
+            return (
+                TypeError(
+                    f"The `{function_kind}` function must be callable, not a raised exception."
+                ),
+                True,
+                None,
             )
 
         try:
             # TODO: technically any sort of exception could be raised here, since
             # depickling is basically involves code execution from the *user*.
             function = from_grpc(function)
-        except SerializationError:
-            yield from self.log(traceback.format_exc(), level=LogLevel.ERROR)
-            raise AbortException(
-                f"The {function_kind} function could not be deserialized."
-            )
+        except SerializationError as exc:
+            return exc, True, traceback.format_exc()
 
         if not callable(function):
-            raise AbortException(
-                f"The {function_kind} function must be callable, not {type(function).__name__}."
+            return (
+                TypeError(
+                    f"The {function_kind} function must be callable, not {type(function).__name__}."
+                ),
+                True,
+                None,
             )
 
         yield from self.log(f"Starting the execution of the {function_kind} function.")