diff --git a/src/wp-includes/general-template.php b/src/wp-includes/general-template.php
index e418f7220a..db0dfafa74 100644
--- a/src/wp-includes/general-template.php
+++ b/src/wp-includes/general-template.php
@@ -2265,10 +2265,9 @@ function get_the_modified_date( $d = '', $post = null ) {
 	$post = get_post( $post );
 
 	if ( ! $post ) {
-		return false;
-	}
-
-	if ( empty( $d ) ) {
+		// For backward compatibility, failures go through the filter below.
+		$the_time = false;
+	} elseif ( empty( $d ) ) {
 		$the_time = get_post_modified_time( get_option( 'date_format' ), false, $post, true );
 	} else {
 		$the_time = get_post_modified_time( $d, false, $post, true );
@@ -2421,10 +2420,9 @@ function get_the_modified_time( $d = '', $post = null ) {
 	$post = get_post( $post );
 
 	if ( ! $post ) {
-		return false;
-	}
-
-	if ( empty( $d ) ) {
+		// For backward compatibility, failures go through the filter below.
+		$the_time = false;
+	} elseif ( empty( $d ) ) {
 		$the_time = get_post_modified_time( get_option( 'time_format' ), false, $post, true );
 	} else {
 		$the_time = get_post_modified_time( $d, false, $post, true );
diff --git a/tests/phpunit/tests/general/template.php b/tests/phpunit/tests/general/template.php
index 0fa6d9c93c..d189cc9449 100644
--- a/tests/phpunit/tests/general/template.php
+++ b/tests/phpunit/tests/general/template.php
@@ -369,6 +369,106 @@ class Tests_General_Template extends WP_UnitTestCase {
 		$this->assertEquals( $expected, $actual );
 	}
 
+	/**
+	 * Test get_the_modified_time failures are filtered
+	 *
+	 * @ticket 37059
+	 *
+	 * @since 4.6.0
+	 */
+	function test_get_the_modified_time_failures_are_filtered() {
+		// Remove global post objet
+		$GLOBALS['post'] = null;
+
+		$expected = 'filtered modified time failure result';
+		add_filter( 'get_the_modified_time', array( $this, '_filter_get_the_modified_time_failure' ) );
+		$actual = get_the_modified_time();
+		$this->assertEquals( $expected, $actual );
+		remove_filter( 'get_the_modified_time', array( $this, '_filter_get_the_modified_time_failure' ) );
+	}
+
+	function _filter_get_the_modified_time_failure( $the_time ) {
+		$expected = false;
+		$actual   = $the_time;
+		$this->assertEquals( $expected, $actual );
+
+		if ( false === $the_time ) {
+			return 'filtered modified time failure result';
+		}
+		return $the_time;
+	}
+
+	/**
+	 * Test get_the_modified_time with post_id parameter.
+	 *
+	 * @ticket 37059
+	 *
+	 * @since 4.6.0
+	 */
+	function test_get_the_modified_date_with_post_id() {
+		$details = array(
+				'post_date' => '2016-01-21 15:34:36',
+				'post_date_gmt' => '2016-01-21 15:34:36',
+		);
+		$post_id = $this->factory->post->create( $details );
+		$d = 'Y-m-d';
+		$expected = '2016-01-21';
+		$actual = get_the_modified_date( $d, $post_id );
+		$this->assertEquals( $expected, $actual );
+	}
+
+	/**
+	 * Test get_the_modified_date
+	 *
+	 * @ticket 37059
+	 *
+	 * @since 4.6.0
+	 */
+	function test_get_the_modified_date_default() {
+		$details = array(
+				'post_date' => '2016-01-21 15:34:36',
+				'post_date_gmt' => '2016-01-21 15:34:36',
+		);
+		$post_id = $this->factory->post->create( $details );
+		$post = get_post( $post_id );
+
+		$GLOBALS['post'] = $post;
+
+		$expected = '2016-01-21';
+		$d = 'Y-m-d';
+		$actual = get_the_modified_date( $d );
+		$this->assertEquals( $expected, $actual );
+	}
+
+	/**
+	 * Test get_the_modified_date failures are filtered
+	 *
+	 * @ticket 37059
+	 *
+	 * @since 4.6.0
+	 */
+	function test_get_the_modified_date_failures_are_filtered() {
+		// Remove global post objet
+		$GLOBALS['post'] = null;
+
+		$expected = 'filtered modified date failure result';
+		add_filter( 'get_the_modified_date', array( $this, '_filter_get_the_modified_date_failure' ) );
+		$actual = get_the_modified_date();
+		$this->assertEquals( $expected, $actual );
+		remove_filter( 'get_the_modified_date', array( $this, '_filter_get_the_modified_date_failure' ) );
+	}
+
+	function _filter_get_the_modified_date_failure( $the_date ) {
+		$expected = false;
+		$actual   = $the_date;
+		$this->assertEquals( $expected, $actual );
+
+		if ( false === $the_date ) {
+			return 'filtered modified date failure result';
+		}
+		return $the_date;
+	}
+
 	/**
 	 * Test get_the_modified_time with post_id parameter.
 	 *