diff --git a/datafusion/optimizer/src/propagate_empty_relation.rs b/datafusion/optimizer/src/propagate_empty_relation.rs
index bd96c558613a..f9183c467f62 100644
--- a/datafusion/optimizer/src/propagate_empty_relation.rs
+++ b/datafusion/optimizer/src/propagate_empty_relation.rs
@@ -210,11 +210,21 @@ impl OptimizerRule for PropagateEmptyRelation {
                     if child.schema().eq(plan.schema()) {
                         Ok(Transformed::yes(child))
                     } else {
+                        // The union takes its field names from its first
+                        // input, which may be gone. Map the remaining
+                        // input's columns by position.
+                        let exprs = child
+                            .schema()
+                            .columns()
+                            .into_iter()
+                            .zip(plan.schema().iter())
+                            .map(|(col, (qualifier, field))| {
+                                Expr::Column(col)
+                                    .alias_qualified(qualifier.cloned(), field.name())
+                            })
+                            .collect::<Vec<_>>();
                         Ok(Transformed::yes(LogicalPlan::Projection(
-                            Projection::new_from_schema(
-                                Arc::new(child),
-                                Arc::clone(plan.schema()),
-                            ),
+                            Projection::try_new(exprs, Arc::new(child))?,
                         )))
                     }
                 } else {
@@ -439,7 +449,8 @@ mod tests {
 
         let plan = LogicalPlanBuilder::from(left).union(right)?.build()?;
 
-        let expected = "Projection: a, b, c\n  TableScan: test";
+        let expected =
+            "Projection: test.a AS a, test.b AS b, test.c AS c\n  TableScan: test";
         assert_together_optimized_plan(plan, expected, true)
     }
 
@@ -529,7 +540,34 @@ mod tests {
 
         let plan = LogicalPlanBuilder::from(left).union(right)?.build()?;
 
-        let expected = "Projection: a, b, c\n  TableScan: test";
+        let expected =
+            "Projection: test.a AS a, test.b AS b, test.c AS c\n  TableScan: test";
+        assert_together_optimized_plan(plan, expected, true)
+    }
+
+    #[test]
+    fn propagate_union_remaining_input_with_other_names() -> Result<()> {
+        // Union
+        //  Filter: false
+        //    TableScan: test
+        //  Projection: test2.a AS x, test2.b AS y, test2.c AS z
+        //    TableScan: test2
+        let left = LogicalPlanBuilder::from(test_table_scan()?)
+            .filter(lit(false))?
+            .build()?;
+        let right = LogicalPlanBuilder::from(test_table_scan_with_name("test2")?)
+            .project(vec![
+                col("a").alias("x"),
+                col("b").alias("y"),
+                col("c").alias("z"),
+            ])?
+            .build()?;
+
+        let plan = LogicalPlanBuilder::from(left).union(right)?.build()?;
+
+        let expected = "Projection: x AS a, y AS b, z AS c\
+        \n  Projection: test2.a AS x, test2.b AS y, test2.c AS z\
+        \n    TableScan: test2";
         assert_together_optimized_plan(plan, expected, true)
     }
 
@@ -813,7 +851,7 @@ mod tests {
             .union(three)?
             .build()?;
 
-        let expected = "Projection: a, b, c\
+        let expected = "Projection: test.a AS a, test.b AS b, test.c AS c\
         \n  TableScan: test";
 
         assert_together_optimized_plan(plan, expected, true)
diff --git a/datafusion/sqllogictest/test_files/struct.slt b/datafusion/sqllogictest/test_files/struct.slt
index 6e0e1b483b1e..5b2ef30b200f 100644
--- a/datafusion/sqllogictest/test_files/struct.slt
+++ b/datafusion/sqllogictest/test_files/struct.slt
@@ -1982,8 +1982,8 @@ statement ok
 drop table rename_swap_struct_field;
 
 # Merging an extraction projection into a projection whose output lost its
-# qualifier. Eliminating the empty side of the union leaves a projection of
-# bare column names over a qualified input, and the merge used to add the
+# qualifier. Eliminating the empty side of the union leaves a projection that
+# renames qualified input columns to bare names, and the merge used to add the
 # pass-through columns under those bare names beside the qualified ones the
 # projection already carried, which is an ambiguous schema.
 statement ok
@@ -2009,7 +2009,7 @@ logical_plan
 03)----Aggregate: groupBy=[[expanded.env]], aggr=[[sum(CAST(__datafusion_extracted_1 AS Int64))]]
 04)------SubqueryAlias: expanded
 05)--------SubqueryAlias: samples
-06)----------Projection: leaf_merge_source.env, get_field(s, Utf8("a")) AS __datafusion_extracted_1
+06)----------Projection: leaf_merge_source.env, get_field(leaf_merge_source.s, Utf8("a")) AS __datafusion_extracted_1
 07)------------TableScan: leaf_merge_source projection=[s, env]
 
 statement ok
diff --git a/datafusion/sqllogictest/test_files/union.slt b/datafusion/sqllogictest/test_files/union.slt
index 2c706596b540..e5694327624c 100644
--- a/datafusion/sqllogictest/test_files/union.slt
+++ b/datafusion/sqllogictest/test_files/union.slt
@@ -1144,6 +1144,20 @@ query TITT
 ----
 ns3 4 t3 m
 
+# repro for https://github.com/apache/datafusion/issues/26516
+# should not error when only a later union input remains
+query I
+SELECT 1 WHERE false UNION ALL (SELECT 2 LIMIT 1);
+----
+2
+
+query I
+SELECT a FROM (VALUES (1)) t(a) WHERE false
+UNION ALL
+(SELECT b FROM (VALUES (2)) s(b) LIMIT 1);
+----
+2
+
 # Config reset
 statement ok
 RESET datafusion.execution.batch_size;