diff --git a/packages/core/src/result.ts b/packages/core/src/result.ts
index 302f7d56c..062f2f079 100644
--- a/packages/core/src/result.ts
+++ b/packages/core/src/result.ts
@@ -115,6 +115,7 @@ class Result implements Promise<QueryResult> {
   private _connectionHolder: connectionHolder.ConnectionHolder
   private _keys: string[] | null
   private _summary: ResultSummary | null
+  private _error: Error | null
   private _watermarks: { high: number; low: number }
 
   /**
@@ -141,6 +142,7 @@ class Result implements Promise<QueryResult> {
     this._connectionHolder = connectionHolder || EMPTY_CONNECTION_HOLDER
     this._keys = null
     this._summary = null
+    this._error = null
     this._watermarks = watermarks
   }
 
@@ -154,8 +156,10 @@ class Result implements Promise<QueryResult> {
    }
    */
   keys(): Promise<string[]> {
-    if (this._keys != null) {
+    if (this._keys !== null) {
       return Promise.resolve(this._keys)
+    } else if (this._error !==  null) {
+      return Promise.reject(this._error)
     }
     return new Promise((resolve, reject) => {
       this._streamObserverPromise
@@ -179,8 +183,10 @@ class Result implements Promise<QueryResult> {
    *
    */
   summary(): Promise<ResultSummary> {
-    if (this._summary != null) {
+    if (this._summary !== null) {
       return Promise.resolve(this._summary)
+    } else if (this._error !== null) {
+      return Promise.reject(this._error)
     }
     return new Promise((resolve, reject) => {
       this._streamObserverPromise
@@ -405,6 +411,7 @@ class Result implements Promise<QueryResult> {
       // and result can't bee consumed any further; call the original onError callback after that
       this._connectionHolder.releaseConnection().then(() => {
         replaceStacktrace(error, this._stack)
+        this._error = error
         onErrorOriginal.call(observer, error)
       })
     }
@@ -431,7 +438,9 @@ class Result implements Promise<QueryResult> {
    * @returns {void}
    */
   _cancel(): void {
-    this._streamObserverPromise.then(o => o.cancel())
+    if (this._summary === null && this._error === null) {
+      this._streamObserverPromise.then(o => o.cancel())
+    }
   }
 
   /**
diff --git a/packages/core/src/session.ts b/packages/core/src/session.ts
index 3c7598a40..bd7ad4424 100644
--- a/packages/core/src/session.ts
+++ b/packages/core/src/session.ts
@@ -64,7 +64,7 @@ class Session {
   private _databaseNameResolved: boolean
   private _lowRecordWatermark: number
   private _highRecordWatermark: number
-
+  private _results: Result[]
   /**
    * @constructor
    * @protected
@@ -128,6 +128,7 @@ class Session {
     const calculatedWatermaks = this._calculateWatermaks()
     this._lowRecordWatermark = calculatedWatermaks.low
     this._highRecordWatermark = calculatedWatermaks.high
+    this._results = []
   }
 
   /**
@@ -154,7 +155,7 @@ class Session {
       ? new TxConfig(transactionConfig)
       : TxConfig.empty()
 
-    return this._run(validatedQuery, params, connection => {
+    const result = this._run(validatedQuery, params, connection => {
       this._assertSessionIsOpen()
       return (connection as Connection).protocol().run(validatedQuery, params, {
         bookmarks: this._lastBookmarks,
@@ -169,6 +170,8 @@ class Session {
         highRecordWatermark: this._highRecordWatermark
       })
     })
+    this._results.push(result)
+    return result
   }
 
   _run(
@@ -415,6 +418,9 @@ class Session {
   async close(): Promise<void> {
     if (this._open) {
       this._open = false
+
+      this._results.forEach(result => result._cancel())
+
       this._transactionExecutor.close()
 
       await this._readConnectionHolder.close()
diff --git a/packages/core/test/result.test.ts b/packages/core/test/result.test.ts
index 674734394..ed8a8e70a 100644
--- a/packages/core/test/result.test.ts
+++ b/packages/core/test/result.test.ts
@@ -59,6 +59,26 @@ describe('Result', () => {
         expect(keys).toBe(expectedKeys)
       })
 
+      it('should reject pre-existing errors', () => {
+        const expectedError = newError('some error')
+        streamObserverMock.onError(expectedError)
+
+        expect(result.keys()).rejects.toBe(expectedError)
+      })
+
+      it('should reject already consumed pre-existing error', async () => {
+        const expectedError = newError('some error')
+        streamObserverMock.onError(expectedError)
+
+        try {
+          await result
+        } catch (e) {
+          // ignore
+        }
+
+        expect(result.keys()).rejects.toBe(expectedError)
+      })
+
       it('should resolve key pushed afterwards', done => {
         const expectedKeys = ['a', 'c']
 
@@ -154,6 +174,26 @@ describe('Result', () => {
           expect(summary).toEqual(expectedSummary)
         })
 
+        it('should reject a pre-existing error', () => {
+          const expectedError = newError('the expected error')
+          streamObserverMock.onError(expectedError)
+
+          expect(result.summary()).rejects.toThrow(expectedError)
+        })
+
+        it('should reject already consumed pre-existing error', async () => {
+          const expectedError = newError('the expected error')
+          streamObserverMock.onError(expectedError)
+
+          try {
+            await result
+          } catch (_) {
+            // ignore
+          }
+
+          expect(result.summary()).rejects.toThrow(expectedError)
+        })
+
         it('should resolve summary pushe afterwards', done => {
           const metadata = {
             resultConsumedAfter: 20,
diff --git a/packages/core/test/session.test.ts b/packages/core/test/session.test.ts
index bf49bba1b..3976dfee1 100644
--- a/packages/core/test/session.test.ts
+++ b/packages/core/test/session.test.ts
@@ -204,6 +204,38 @@ describe('session', () => {
     })
   }, 70000)
 
+  it('should call cancel current result', done => {
+    const session = newSessionWithConnection(newFakeConnection())
+
+    const result = session.run('RETURN 1')
+    const spiedCancel =  jest.spyOn(result, '_cancel')
+
+    session.close()
+      .finally(() => {
+        expect(spiedCancel).toHaveBeenCalled()
+        done()
+      })
+  })
+
+  it('should call cancel current results', done => {
+    const session = newSessionWithConnection(newFakeConnection())
+
+    const spiedCancels: any[] = []
+
+    for (let i = 0; i < 10; i++) {
+      const result = session.run('RETURN 1')
+      spiedCancels.push(jest.spyOn(result, '_cancel'))
+    }
+
+    session.close()
+      .finally(() => {
+        spiedCancels.forEach(spy => {
+          expect(spy).toHaveBeenCalled()
+        })
+        done()
+      })
+  })
+
   describe('.lastBookmark()', () => {
     it.each([
       [bookmarks.Bookmarks.empty()],
diff --git a/packages/neo4j-driver/test/session.test.js b/packages/neo4j-driver/test/session.test.js
index 13c320c4d..920c3ec32 100644
--- a/packages/neo4j-driver/test/session.test.js
+++ b/packages/neo4j-driver/test/session.test.js
@@ -341,7 +341,7 @@ describe('#integration session', () => {
               'Query failed after a long running query was terminated',
               error
             )
-            done.fail.bind(done)
+            done.fail(error)
           })
       })