diff --git a/thunder/tests/test_core.py b/thunder/tests/test_core.py
index fd751939b8..09c5e81baa 100644
--- a/thunder/tests/test_core.py
+++ b/thunder/tests/test_core.py
@@ -2819,3 +2819,35 @@ def foo(x):
     expected = foo(TestDataclass(t, s))
 
     torch.testing.assert_close(actual, expected)
+
+
+@pytest.mark.filterwarnings("ignore:Please use `torch.vmap`")
+def test_custom_autograd_function():
+    from torch.autograd.gradcheck import GradcheckError
+    from torch.testing._internal.common_utils import gradcheck
+
+    class MyFunction(torch.autograd.Function):
+
+        @staticmethod
+        def forward(ctx, x: torch.Tensor) -> torch.Tensor:
+            return x * 2.0
+
+        # this is wrong on purpose.
+        @staticmethod
+        def backward(ctx, grad_output) -> torch.Tensor:
+            return grad_output
+
+    class Model(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x) -> torch.Tensor:
+            return MyFunction.apply(x)
+
+    x = torch.randn((2, 2), dtype=torch.float64, requires_grad=True)
+    model = Model().to(dtype=torch.float64)
+    jitted = thunder.jit(model, skip_inplace_functionalization=True)
+
+    gradcheck(jitted, (x,))
+    with pytest.raises(GradcheckError):
+        gradcheck(model, (x,))
diff --git a/thunder/torch/__init__.py b/thunder/torch/__init__.py
index 04ccd74628..613443d942 100644
--- a/thunder/torch/__init__.py
+++ b/thunder/torch/__init__.py
@@ -17,6 +17,7 @@
 # Initializes the language context
 from thunder.torch.langctx import register_method, register_property
 
+from thunder.core.baseutils import run_once
 import thunder.clang as clang
 import thunder.core.devices as devices
 from thunder.core.devices import to_device, device_from_string
@@ -4936,6 +4937,24 @@ def _set_grad_enabled_with_warning(enabled: bool) -> None:
 register_function(torch._C._set_grad_enabled, _set_grad_enabled_with_warning)
 
 
+@run_once
+def _warn_for_unwrap_if_dead():
+    warnings.warn(
+        "torch._C._functorch.unwrap_if_dead has no effect under thunder.jit. "
+        "`torch.autograd.Function.backward` is not respected by `thunder.jit`. "
+        "`thunder.jit` generates backward based on the forward"
+    )
+
+
+def _unwrap_if_dead(tensor):
+
+    _warn_for_unwrap_if_dead()
+    return tensor
+
+
+register_function(torch._C._functorch.unwrap_if_dead, _unwrap_if_dead)
+
+
 #
 # Distributed operations
 #