diff --git a/Lib/test/test_resource.py b/Lib/test/test_resource.py
index 5fd076bee38e79..0e1738ef0ad04a 100644
--- a/Lib/test/test_resource.py
+++ b/Lib/test/test_resource.py
@@ -50,47 +50,49 @@ def test_fsize_ismax(self):
                      "setting RLIMIT_FSIZE is not supported on VxWorks")
     @unittest.skipUnless(hasattr(resource, 'RLIMIT_FSIZE'), 'requires resource.RLIMIT_FSIZE')
     def test_fsize_enforced(self):
-        (cur, max) = resource.getrlimit(resource.RLIMIT_FSIZE)
-        # Check to see what happens when the RLIMIT_FSIZE is small.  Some
-        # versions of Python were terminated by an uncaught SIGXFSZ, but
-        # pythonrun.c has been fixed to ignore that exception.  If so, the
-        # write() should return EFBIG when the limit is exceeded.
+        try:
+            (cur, max_lim) = resource.getrlimit(resource.RLIMIT_FSIZE)
+        except OSError as e:
+            self.skipTest(f"getrlimit(RLIMIT_FSIZE) failed: {e}")
+
+        if max_lim != resource.RLIM_INFINITY and max_lim < 1025:
+            self.skipTest(f"system RLIMIT_FSIZE hard limit ({max_lim}) is too small for this test")
 
-        # At least one platform has an unlimited RLIMIT_FSIZE and attempts
-        # to change it raise ValueError instead.
         try:
+            resource.setrlimit(resource.RLIMIT_FSIZE, (1024, max_lim))
+            resource.setrlimit(resource.RLIMIT_FSIZE, (cur, max_lim))
+        except (ValueError, OSError, PermissionError) as e:
+            self.skipTest(f"cannot set RLIMIT_FSIZE to 1024: {e}")
+
+        self.addCleanup(os_helper.unlink, os_helper.TESTFN)
+        self.addCleanup(resource.setrlimit, resource.RLIMIT_FSIZE, (cur, max_lim))
+
+        resource.setrlimit(resource.RLIMIT_FSIZE, (1024, max_lim))
+
+        f = open(os_helper.TESTFN, "wb")
+        try:
+            f.write(b"X" * 1024)
             try:
-                resource.setrlimit(resource.RLIMIT_FSIZE, (1024, max))
-                limit_set = True
-            except ValueError:
-                limit_set = False
-            f = open(os_helper.TESTFN, "wb")
-            try:
-                f.write(b"X" * 1024)
-                try:
-                    f.write(b"Y")
+                f.write(b"Y")
+                f.flush()
+                # On some systems (e.g., Ubuntu on hppa) the flush()
+                # doesn't always cause the exception, but the close()
+                # does eventually.  Try flushing several times in
+                # an attempt to ensure the file is really synced and
+                # the exception raised.
+                for i in range(5):
+                    time.sleep(.1)
                     f.flush()
-                    # On some systems (e.g., Ubuntu on hppa) the flush()
-                    # doesn't always cause the exception, but the close()
-                    # does eventually.  Try flushing several times in
-                    # an attempt to ensure the file is really synced and
-                    # the exception raised.
-                    for i in range(5):
-                        time.sleep(.1)
-                        f.flush()
-                except OSError:
-                    if not limit_set:
-                        raise
-                if limit_set:
-                    # Close will attempt to flush the byte we wrote
-                    # Restore limit first to avoid getting a spurious error
-                    resource.setrlimit(resource.RLIMIT_FSIZE, (cur, max))
-            finally:
-                f.close()
+            except OSError:
+                pass
+            else:
+                self.fail("f.write() did not raise OSError when exceeding RLIMIT_FSIZE")
+
+            # Close will attempt to flush the byte we wrote
+            # Restore limit first to avoid getting a spurious error
+            resource.setrlimit(resource.RLIMIT_FSIZE, (cur, max_lim))
         finally:
-            if limit_set:
-                resource.setrlimit(resource.RLIMIT_FSIZE, (cur, max))
-            os_helper.unlink(os_helper.TESTFN)
+            f.close()
 
     @unittest.skipIf(sys.platform == "vxworks",
                      "setting RLIMIT_FSIZE is not supported on VxWorks")
diff --git a/Misc/NEWS.d/next/Tests/2026-03-06-09-43-49.gh-issue-37883.I-3oZq.rst b/Misc/NEWS.d/next/Tests/2026-03-06-09-43-49.gh-issue-37883.I-3oZq.rst
new file mode 100644
index 00000000000000..a047b69646c4ab
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2026-03-06-09-43-49.gh-issue-37883.I-3oZq.rst
@@ -0,0 +1 @@
+Fix ``test_resource.test_fsize_enforced`` to gracefully skip when the system hard limit or privileges prevent setting file size limits.