diff --git a/crossplane/function/resource.py b/crossplane/function/resource.py
index 039af46..c9bfc69 100644
--- a/crossplane/function/resource.py
+++ b/crossplane/function/resource.py
@@ -45,8 +45,8 @@ def update(r: fnv1.Resource, source: dict | structpb.Struct | pydantic.BaseModel
             # apiVersion is set to its default value 's3.aws.upbound.io/v1beta2'
             # (and not explicitly provided during initialization), it will be
             # excluded from the serialized output.
-            data['apiVersion'] = source.apiVersion
-            data['kind'] = source.kind
+            data["apiVersion"] = source.apiVersion
+            data["kind"] = source.kind
             r.resource.update(data)
         case structpb.Struct():
             # TODO(negz): Use struct_to_dict and update to match other semantics?
diff --git a/crossplane/function/runtime.py b/crossplane/function/runtime.py
index f91f392..3783bbc 100644
--- a/crossplane/function/runtime.py
+++ b/crossplane/function/runtime.py
@@ -16,6 +16,7 @@
 
 import asyncio
 import os
+import signal
 
 import grpc
 from grpc_reflection.v1alpha import reflection
@@ -25,6 +26,7 @@
 import crossplane.function.proto.v1beta1.run_function_pb2 as fnv1beta1
 import crossplane.function.proto.v1beta1.run_function_pb2_grpc as grpcv1beta1
 
+GRACE_PERIOD = 5
 SERVICE_NAMES = (
     reflection.SERVICE_NAME,
     fnv1.DESCRIPTOR.services_by_name["FunctionRunnerService"].full_name,
@@ -64,6 +66,10 @@ def load_credentials(tls_certs_dir: str) -> grpc.ServerCredentials:
     )
 
 
+async def _stop(server, grace=GRACE_PERIOD):
+    await server.stop(grace=grace)
+
+
 def serve(
     function: grpcv1.FunctionRunnerService,
     address: str,
@@ -90,6 +96,11 @@ def serve(
 
     server = grpc.aio.server()
 
+    signal.signal(
+        signal.SIGTERM,
+        lambda _, __: asyncio.create_task(_stop(server)),
+    )
+
     grpcv1.add_FunctionRunnerServiceServicer_to_server(function, server)
     grpcv1beta1.add_FunctionRunnerServiceServicer_to_server(
         BetaFunctionRunner(wrapped=function), server
@@ -116,7 +127,8 @@ async def start():
     try:
         loop.run_until_complete(start())
     finally:
-        loop.run_until_complete(server.stop(grace=5))
+        if server._server.is_running():
+            loop.run_until_complete(server.stop(grace=GRACE_PERIOD))
         loop.close()
 
 
diff --git a/tests/test_runtime.py b/tests/test_runtime.py
index 26229aa..5c31269 100644
--- a/tests/test_runtime.py
+++ b/tests/test_runtime.py
@@ -12,7 +12,10 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+import asyncio
 import dataclasses
+import os
+import signal
 import unittest
 
 import grpc
@@ -52,6 +55,25 @@ class TestCase:
 
             self.assertEqual(rsp, case.want, "-want, +got")
 
+    async def test_sigterm_handling(self) -> None:
+        async def mock_server():
+            await server.start()
+            await asyncio.sleep(1)
+            self.assertTrue(server._server.is_running(), "Server should be running")
+            os.kill(os.getpid(), signal.SIGTERM)
+            await server.wait_for_termination()
+            self.assertFalse(
+                server._server.is_running(),
+                "Server should have been stopped on SIGTERM",
+            )
+
+        server = grpc.aio.server()
+        signal.signal(
+            signal.SIGTERM,
+            lambda _, __: asyncio.create_task(runtime._stop(server)),
+        )
+        await mock_server()
+
 
 class EchoRunner(grpcv1.FunctionRunnerService):
     def __init__(self):