diff --git a/mlir/lib/Transforms/Utils/DialectConversion.cpp b/mlir/lib/Transforms/Utils/DialectConversion.cpp
--- a/mlir/lib/Transforms/Utils/DialectConversion.cpp
+++ b/mlir/lib/Transforms/Utils/DialectConversion.cpp
@@ -1147,6 +1147,8 @@
                        block, converter, *conversion, mapping, argReplacements)
                  : argConverter.convertSignature(block, converter, mapping,
                                                  argReplacements);
+  if (failed(result))
+    return failure();
   if (Block *newBlock = result.getValue()) {
     if (newBlock != block)
       blockActions.push_back(BlockAction::getTypeConversion(newBlock));
diff --git a/mlir/test/Transforms/test-legalize-type-conversion.mlir b/mlir/test/Transforms/test-legalize-type-conversion.mlir
--- a/mlir/test/Transforms/test-legalize-type-conversion.mlir
+++ b/mlir/test/Transforms/test-legalize-type-conversion.mlir
@@ -99,3 +99,17 @@
   }) : () -> ()
   return
 }
+
+// -----
+
+// Should not segfault here but gracefully fail.
+// CHECK-LABEL: func @test_block_argument_not_converted
+func @test_block_argument_not_converted() {
+  "test.unsupported_block_arg_type"() ({
+    // NOTE: The test pass does not convert `index` types.
+    // CHECK: ^bb0({{.*}}: index):
+    ^bb0(%0 : index):
+      "test.return"(%0) : (index) -> ()
+  }) : () -> ()
+  return
+}