diff --git a/spec/Subscription-spec.ts b/spec/Subscription-spec.ts
index b19f37a487..32143cfa0c 100644
--- a/spec/Subscription-spec.ts
+++ b/spec/Subscription-spec.ts
@@ -116,7 +116,7 @@ describe('Subscription', () => {
   });
 
   describe('unsubscribe()', () => {
-    it('Should unsubscribe from all subscriptions, when some of them throw', (done) => {
+    it('should unsubscribe from all subscriptions, when some of them throw', (done) => {
       const tearDowns: number[] = [];
 
       const source1 = new Observable(() => {
@@ -149,7 +149,7 @@ describe('Subscription', () => {
       });
     });
 
-    it('Should unsubscribe from all subscriptions, when adding a bad custom subscription to a subscription', (done) => {
+    it('should unsubscribe from all subscriptions, when adding a bad custom subscription to a subscription', (done) => {
       const tearDowns: number[] = [];
 
       const sub = new Subscription();
@@ -189,7 +189,7 @@ describe('Subscription', () => {
       });
     });
 
-    it('Should have idempotent unsubscription', () => {
+    it('should have idempotent unsubscription', () => {
       let count = 0;
       const subscription = new Subscription(() => ++count);
       expect(count).to.equal(0);
@@ -200,5 +200,28 @@ describe('Subscription', () => {
       subscription.unsubscribe();
       expect(count).to.equal(1);
     });
+
+    it('should unsubscribe from all parents', () => {
+      // https://github.com/ReactiveX/rxjs/issues/6351
+      const a = new Subscription(() => { /* noop */});
+      const b = new Subscription(() => { /* noop */});
+      const c = new Subscription(() => { /* noop */});
+      const d = new Subscription(() => { /* noop */});
+      a.add(d);
+      b.add(d);
+      c.add(d);
+      // When d is added to the subscriptions, it's added as a teardown. The
+      // length is 1 because the teardowns passed to the ctors are stored in a
+      // separate property.
+      expect((a as any)._teardowns).to.have.length(1);
+      expect((b as any)._teardowns).to.have.length(1);
+      expect((c as any)._teardowns).to.have.length(1);
+      d.unsubscribe();
+      // When d is unsubscribed, it should remove itself from each of its
+      // parents.
+      expect((a as any)._teardowns).to.have.length(0);
+      expect((b as any)._teardowns).to.have.length(0);
+      expect((c as any)._teardowns).to.have.length(0);
+    });
   });
 });
diff --git a/src/internal/Subscription.ts b/src/internal/Subscription.ts
index 4192bdabaa..9ff58e72da 100644
--- a/src/internal/Subscription.ts
+++ b/src/internal/Subscription.ts
@@ -56,12 +56,15 @@ export class Subscription implements SubscriptionLike {
 
       // Remove this from it's parents.
       const { _parentage } = this;
-      if (Array.isArray(_parentage)) {
-        for (const parent of _parentage) {
-          parent.remove(this);
+      if (_parentage) {
+        this._parentage = null;
+        if (Array.isArray(_parentage)) {
+          for (const parent of _parentage) {
+            parent.remove(this);
+          }
+        } else {
+          _parentage.remove(this);
         }
-      } else {
-        _parentage?.remove(this);
       }
 
       const { initialTeardown } = this;