diff --git a/core/src/main/java/ai/timefold/solver/core/impl/heuristic/selector/list/ElementLocationRandomIterator.java b/core/src/main/java/ai/timefold/solver/core/impl/heuristic/selector/list/ElementLocationRandomIterator.java
index 3ac48f98c2..d340eff2bb 100644
--- a/core/src/main/java/ai/timefold/solver/core/impl/heuristic/selector/list/ElementLocationRandomIterator.java
+++ b/core/src/main/java/ai/timefold/solver/core/impl/heuristic/selector/list/ElementLocationRandomIterator.java
@@ -52,8 +52,10 @@ public ElementLocation next() {
         // This code operates under the assumption that the entity selector already filtered out all immovable entities.
         // At this point, entities are only partially pinned, or not pinned at all.
         var entitySize = entitySelector.getSize();
+        // If we support unassigned values, we have to add 1 to all the sizes
+        // to account for the unassigned destination, which is an extra element.
         var entityBoundary = allowsUnassignedValues ? entitySize + 1 : entitySize;
-        long random = RandomUtils.nextLong(workingRandom, totalSize);
+        var random = RandomUtils.nextLong(workingRandom, allowsUnassignedValues ? totalSize + 1 : totalSize);
         if (allowsUnassignedValues && random == 0) {
             // We have already excluded all unassigned elements,
             // the only way to get an unassigned destination is to explicitly add it.
@@ -75,11 +77,11 @@ public ElementLocation next() {
                 // This skews the selection probability towards entities with fewer unpinned values,
                 // but at this point, there is no other thing we could possibly do.
                 var entity = entityIterator.next();
-                int unpinnedSize = listVariableDescriptor.getUnpinnedSubListSize(entity);
+                var unpinnedSize = listVariableDescriptor.getUnpinnedSubListSize(entity);
                 if (unpinnedSize == 0) { // Only the last destination remains.
                     return ElementLocation.of(entity, listVariableDescriptor.getListSize(entity));
                 } else { // +1 to include the destination after the final element in the list.
-                    int randomIndex = workingRandom.nextInt(unpinnedSize + 1);
+                    var randomIndex = workingRandom.nextInt(unpinnedSize + 1);
                     return ElementLocation.of(entity, listVariableDescriptor.getFirstUnpinnedIndex(entity) + randomIndex);
                 }
             } else { // +1 to include the destination after the final element in the list.
diff --git a/core/src/test/java/ai/timefold/solver/core/impl/heuristic/selector/list/ElementDestinationSelectorTest.java b/core/src/test/java/ai/timefold/solver/core/impl/heuristic/selector/list/ElementDestinationSelectorTest.java
index c6f923c774..6195cdb5d7 100644
--- a/core/src/test/java/ai/timefold/solver/core/impl/heuristic/selector/list/ElementDestinationSelectorTest.java
+++ b/core/src/test/java/ai/timefold/solver/core/impl/heuristic/selector/list/ElementDestinationSelectorTest.java
@@ -3,6 +3,7 @@
 import static ai.timefold.solver.core.impl.heuristic.selector.SelectorTestUtils.phaseStarted;
 import static ai.timefold.solver.core.impl.heuristic.selector.SelectorTestUtils.solvingStarted;
 import static ai.timefold.solver.core.impl.heuristic.selector.SelectorTestUtils.stepStarted;
+import static ai.timefold.solver.core.impl.testdata.domain.list.TestdataListUtils.getAllowsUnassignedvaluesListVariableDescriptor;
 import static ai.timefold.solver.core.impl.testdata.domain.list.TestdataListUtils.getListVariableDescriptor;
 import static ai.timefold.solver.core.impl.testdata.domain.list.TestdataListUtils.getPinnedAllowsUnassignedvaluesListVariableDescriptor;
 import static ai.timefold.solver.core.impl.testdata.domain.list.TestdataListUtils.getPinnedListVariableDescriptor;
@@ -19,6 +20,7 @@
 
 import java.util.Collections;
 import java.util.List;
+import java.util.Random;
 
 import ai.timefold.solver.core.config.heuristic.selector.common.SelectionCacheType;
 import ai.timefold.solver.core.impl.heuristic.selector.entity.FromSolutionEntitySelector;
@@ -27,6 +29,9 @@
 import ai.timefold.solver.core.impl.testdata.domain.list.TestdataListEntity;
 import ai.timefold.solver.core.impl.testdata.domain.list.TestdataListSolution;
 import ai.timefold.solver.core.impl.testdata.domain.list.TestdataListValue;
+import ai.timefold.solver.core.impl.testdata.domain.list.allows_unassigned.TestdataAllowsUnassignedValuesListEntity;
+import ai.timefold.solver.core.impl.testdata.domain.list.allows_unassigned.TestdataAllowsUnassignedValuesListSolution;
+import ai.timefold.solver.core.impl.testdata.domain.list.allows_unassigned.TestdataAllowsUnassignedValuesListValue;
 import ai.timefold.solver.core.impl.testdata.domain.list.allows_unassigned.pinned.TestdataPinnedUnassignedValuesListEntity;
 import ai.timefold.solver.core.impl.testdata.domain.list.allows_unassigned.pinned.TestdataPinnedUnassignedValuesListSolution;
 import ai.timefold.solver.core.impl.testdata.domain.list.allows_unassigned.pinned.TestdataPinnedUnassignedValuesListValue;
@@ -202,6 +207,42 @@ void randomPartiallyPinnedAndUnassigned() {
                 "D[3]");
     }
 
+    @Test
+    void randomUnassignedSingleEntity() {
+        var unassignedValue = new TestdataAllowsUnassignedValuesListValue("3");
+        var a = TestdataAllowsUnassignedValuesListEntity.createWithValues("A");
+
+        var solution = new TestdataAllowsUnassignedValuesListSolution();
+        solution.setEntityList(List.of(a));
+        solution.setValueList(List.of(unassignedValue));
+
+        var solutionDescriptor = TestdataAllowsUnassignedValuesListSolution.buildSolutionDescriptor();
+        var scoreDirector = mockScoreDirector(solutionDescriptor);
+        scoreDirector.setWorkingSolution(solution);
+
+        var solverScope = new SolverScope<TestdataAllowsUnassignedValuesListSolution>();
+        solverScope.setScoreDirector(scoreDirector);
+        // This needs to use a real Random instance, otherwise the test never covers the situation where
+        // the random value of 1 needs to be produced to get to the entity.
+        solverScope.setWorkingRandom(new Random(0));
+        var entitySelector = new FromSolutionEntitySelector<>(
+                solutionDescriptor.findEntityDescriptorOrFail(TestdataAllowsUnassignedValuesListEntity.class),
+                SelectionCacheType.PHASE, true);
+        entitySelector.solvingStarted(solverScope);
+        entitySelector.phaseStarted(new LocalSearchPhaseScope<>(solverScope, 0));
+
+        var valueSelector = mockEntityIndependentValueSelector(
+                getAllowsUnassignedvaluesListVariableDescriptor(scoreDirector),
+                unassignedValue);
+        var selector = new ElementDestinationSelector<>(entitySelector, valueSelector, true);
+        selector.solvingStarted(solverScope);
+        selector.phaseStarted(new LocalSearchPhaseScope<>(solverScope, 0));
+
+        assertCodesOfNeverEndingIterator(selector.iterator(),
+                "A[0]", // Ensure the entity is accessible.
+                "UnassignedLocation"); // As well as the unassigned location.
+    }
+
     @Test
     void randomFullyPinned() {
         var v1 = new TestdataPinnedWithIndexListValue("1");