diff --git a/apps/opentelemetry/src/otel_batch_processor.erl b/apps/opentelemetry/src/otel_batch_processor.erl
index dca06d71..945aa133 100644
--- a/apps/opentelemetry/src/otel_batch_processor.erl
+++ b/apps/opentelemetry/src/otel_batch_processor.erl
@@ -319,6 +319,14 @@ terminate(_Reason, _State, #data{exporter=Exporter,
     %% `export' is used to perform a blocking export
     _ = export(Exporter, Resource, CurrentTable),
 
+    %% Synchronously shut the exporter down before this gen_statem exits.
+    %% Linked transport resources (e.g. grpcbox channels) clean up via
+    %% gproc in their own `terminate'; if we just return here, those
+    %% terminations race with the shutdown of the `grpcbox' application
+    %% itself and crash with "the table identifier does not refer to an
+    %% existing ETS table". See open-telemetry/opentelemetry-erlang#868.
+    _ = otel_exporter:shutdown(Exporter),
+
     ok.
 
 %%
diff --git a/apps/opentelemetry/src/otel_simple_processor.erl b/apps/opentelemetry/src/otel_simple_processor.erl
index 8d07e593..26d73dc2 100644
--- a/apps/opentelemetry/src/otel_simple_processor.erl
+++ b/apps/opentelemetry/src/otel_simple_processor.erl
@@ -183,7 +183,12 @@ handle_event_(_, _, _, _) ->
     keep_state_and_data.
 
 %% @private
-terminate(_, _, _Data) ->
+terminate(_, _, #data{exporter=Exporter}) ->
+    %% Synchronously shut the exporter down before this gen_statem exits,
+    %% mirroring `otel_batch_processor:terminate/3'. See #868 — linked
+    %% grpcbox channels crash on a missing `gproc' ETS table when they
+    %% terminate after the `grpcbox' application is already gone.
+    _ = otel_exporter:shutdown(Exporter),
     ok.
 
 %%