diff --git a/src/DataStreams/NativeBlockOutputStream.cpp b/src/DataStreams/NativeBlockOutputStream.cpp
index da68376201f..2a016c9a0c8 100644
--- a/src/DataStreams/NativeBlockOutputStream.cpp
+++ b/src/DataStreams/NativeBlockOutputStream.cpp
@@ -41,7 +41,7 @@ void NativeBlockOutputStream::flush()
 }
 
 
-void NativeBlockOutputStream::writeData(const IDataType & type, const ColumnPtr & column, WriteBuffer & ostr, UInt64 offset, UInt64 limit)
+static void writeData(const IDataType & type, const ColumnPtr & column, WriteBuffer & ostr, UInt64 offset, UInt64 limit)
 {
     /** If there are columns-constants - then we materialize them.
       * (Since the data type does not know how to serialize / deserialize constants.)
diff --git a/src/DataStreams/NativeBlockOutputStream.h b/src/DataStreams/NativeBlockOutputStream.h
index 64ccd267634..c47d7b2f1c3 100644
--- a/src/DataStreams/NativeBlockOutputStream.h
+++ b/src/DataStreams/NativeBlockOutputStream.h
@@ -30,8 +30,6 @@ public:
     void write(const Block & block) override;
     void flush() override;
 
-    static void writeData(const IDataType & type, const ColumnPtr & column, WriteBuffer & ostr, UInt64 offset, UInt64 limit);
-
     String getContentType() const override { return "application/octet-stream"; }
 
 private:
diff --git a/src/Processors/Formats/Impl/ParallelFormattingOutputFormat.cpp b/src/Processors/Formats/Impl/ParallelFormattingOutputFormat.cpp
index 0ebca3661b4..ce7dd1abd51 100644
--- a/src/Processors/Formats/Impl/ParallelFormattingOutputFormat.cpp
+++ b/src/Processors/Formats/Impl/ParallelFormattingOutputFormat.cpp
@@ -80,9 +80,11 @@ namespace DB
     }
 
 
-    void ParallelFormattingOutputFormat::collectorThreadFunction()
+    void ParallelFormattingOutputFormat::collectorThreadFunction(const ThreadGroupStatusPtr & thread_group)
     {
         setThreadName("Collector");
+        if (thread_group)
+            CurrentThread::attachToIfDetached(thread_group);
 
         try
         {
@@ -135,9 +137,11 @@ namespace DB
     }
 
 
-    void ParallelFormattingOutputFormat::formatterThreadFunction(size_t current_unit_number)
+    void ParallelFormattingOutputFormat::formatterThreadFunction(size_t current_unit_number, const ThreadGroupStatusPtr & thread_group)
     {
         setThreadName("Formatter");
+        if (thread_group)
+            CurrentThread::attachToIfDetached(thread_group);
 
         try
         {
diff --git a/src/Processors/Formats/Impl/ParallelFormattingOutputFormat.h b/src/Processors/Formats/Impl/ParallelFormattingOutputFormat.h
index 584aa364d27..8b9e8293c69 100644
--- a/src/Processors/Formats/Impl/ParallelFormattingOutputFormat.h
+++ b/src/Processors/Formats/Impl/ParallelFormattingOutputFormat.h
@@ -76,7 +76,10 @@ public:
         /// Just heuristic. We need one thread for collecting, one thread for receiving chunks
         /// and n threads for formatting.
         processing_units.resize(params.max_threads_for_parallel_formatting + 2);
-        collector_thread = ThreadFromGlobalPool([&] { collectorThreadFunction(); });
+        collector_thread = ThreadFromGlobalPool([thread_group = CurrentThread::getGroup(), this]
+        {
+            collectorThreadFunction(thread_group);
+        });
         LOG_TRACE(&Poco::Logger::get("ParallelFormattingOutputFormat"), "Parallel formatting is being used");
     }
 
@@ -200,14 +203,17 @@ private:
 
     void scheduleFormatterThreadForUnitWithNumber(size_t ticket_number)
     {
-        pool.scheduleOrThrowOnError([this, ticket_number] { formatterThreadFunction(ticket_number); });
+        pool.scheduleOrThrowOnError([this, thread_group = CurrentThread::getGroup(), ticket_number]
+        {
+            formatterThreadFunction(ticket_number, thread_group);
+        });
     }
 
     /// Collects all temporary buffers into main WriteBuffer.
-    void collectorThreadFunction();
+    void collectorThreadFunction(const ThreadGroupStatusPtr & thread_group);
 
     /// This function is executed in ThreadPool and the only purpose of it is to format one Chunk into a continuous buffer in memory.
-    void formatterThreadFunction(size_t current_unit_number);
+    void formatterThreadFunction(size_t current_unit_number, const ThreadGroupStatusPtr & thread_group);
 };
 
 }
diff --git a/src/Server/TCPHandler.cpp b/src/Server/TCPHandler.cpp
index ae9358c6159..efda9bbfec3 100644
--- a/src/Server/TCPHandler.cpp
+++ b/src/Server/TCPHandler.cpp
@@ -1409,22 +1409,49 @@ void TCPHandler::sendData(const Block & block)
 {
     initBlockOutput(block);
 
-    writeVarUInt(Protocol::Server::Data, *out);
-    /// Send external table name (empty name is the main table)
-    writeStringBinary("", *out);
+    auto prev_bytes_written_out = out->count();
+    auto prev_bytes_written_compressed_out = state.maybe_compressed_out->count();
 
-    /// For testing hedged requests
-    const Settings & settings = query_context->getSettingsRef();
-    if (block.rows() > 0 && settings.sleep_in_send_data_ms.totalMilliseconds())
+    try
     {
-        out->next();
-        std::chrono::milliseconds ms(settings.sleep_in_send_data_ms.totalMilliseconds());
-        std::this_thread::sleep_for(ms);
-    }
+        writeVarUInt(Protocol::Server::Data, *out);
+        /// Send external table name (empty name is the main table)
+        writeStringBinary("", *out);
 
-    state.block_out->write(block);
-    state.maybe_compressed_out->next();
-    out->next();
+        /// For testing hedged requests
+        const Settings & settings = query_context->getSettingsRef();
+        if (block.rows() > 0 && settings.sleep_in_send_data_ms.totalMilliseconds())
+        {
+            out->next();
+            std::chrono::milliseconds ms(settings.sleep_in_send_data_ms.totalMilliseconds());
+            std::this_thread::sleep_for(ms);
+        }
+
+        state.block_out->write(block);
+        state.maybe_compressed_out->next();
+        out->next();
+    }
+    catch (...)
+    {
+        /// In case of unsuccessful write, if the buffer with written data was not flushed,
+        ///  we will rollback write to avoid breaking the protocol.
+        /// (otherwise the client will not be able to receive exception after unfinished data
+        ///  as it will expect the continuation of the data).
+        /// It looks like hangs on client side or a message like "Data compressed with different methods".
+
+        if (state.compression == Protocol::Compression::Enable)
+        {
+            auto extra_bytes_written_compressed = state.maybe_compressed_out->count() - prev_bytes_written_compressed_out;
+            if (state.maybe_compressed_out->offset() >= extra_bytes_written_compressed)
+                state.maybe_compressed_out->position() -= extra_bytes_written_compressed;
+        }
+
+        auto extra_bytes_written_out = out->count() - prev_bytes_written_out;
+        if (out->offset() >= extra_bytes_written_out)
+            out->position() -= extra_bytes_written_out;
+
+        throw;
+    }
 }
 
 
diff --git a/tests/queries/0_stateless/01783_parallel_formatting_memory.reference b/tests/queries/0_stateless/01783_parallel_formatting_memory.reference
new file mode 100644
index 00000000000..c5cdc5cf0bb
--- /dev/null
+++ b/tests/queries/0_stateless/01783_parallel_formatting_memory.reference
@@ -0,0 +1 @@
+Code: 241
diff --git a/tests/queries/0_stateless/01783_parallel_formatting_memory.sh b/tests/queries/0_stateless/01783_parallel_formatting_memory.sh
new file mode 100755
index 00000000000..0b8cb0bc6be
--- /dev/null
+++ b/tests/queries/0_stateless/01783_parallel_formatting_memory.sh
@@ -0,0 +1,7 @@
+#!/usr/bin/env bash
+
+CUR_DIR=$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)
+# shellcheck source=../shell_config.sh
+. "$CUR_DIR"/../shell_config.sh
+
+$CLICKHOUSE_CURL -sS "$CLICKHOUSE_URL&max_memory_usage=1G" -d "SELECT range(65535) FROM system.one ARRAY JOIN range(65536) AS number" | grep -oF 'Code: 241'
diff --git a/tests/queries/0_stateless/01784_parallel_formatting_memory.reference b/tests/queries/0_stateless/01784_parallel_formatting_memory.reference
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/tests/queries/0_stateless/01784_parallel_formatting_memory.sql b/tests/queries/0_stateless/01784_parallel_formatting_memory.sql
new file mode 100644
index 00000000000..35dc063f895
--- /dev/null
+++ b/tests/queries/0_stateless/01784_parallel_formatting_memory.sql
@@ -0,0 +1,2 @@
+SET max_memory_usage = '1G';
+SELECT range(65535) FROM system.one ARRAY JOIN range(65536) AS number; -- { serverError 241 }
diff --git a/tests/queries/0_stateless/01785_parallel_formatting_memory.reference b/tests/queries/0_stateless/01785_parallel_formatting_memory.reference
new file mode 100644
index 00000000000..0ec7fc54b01
--- /dev/null
+++ b/tests/queries/0_stateless/01785_parallel_formatting_memory.reference
@@ -0,0 +1,2 @@
+Code: 241
+Code: 241
diff --git a/tests/queries/0_stateless/01785_parallel_formatting_memory.sh b/tests/queries/0_stateless/01785_parallel_formatting_memory.sh
new file mode 100755
index 00000000000..6d081c61fd3
--- /dev/null
+++ b/tests/queries/0_stateless/01785_parallel_formatting_memory.sh
@@ -0,0 +1,8 @@
+#!/usr/bin/env bash
+
+CUR_DIR=$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)
+# shellcheck source=../shell_config.sh
+. "$CUR_DIR"/../shell_config.sh
+
+$CLICKHOUSE_CLIENT --compress 0 --max_memory_usage 1G --query "SELECT range(65535) FROM system.one ARRAY JOIN range(65536) AS number" 2>&1 | grep -oF 'Code: 241' | head -n1
+$CLICKHOUSE_CLIENT --compress 1 --max_memory_usage 1G --query "SELECT range(65535) FROM system.one ARRAY JOIN range(65536) AS number" 2>&1 | grep -oF 'Code: 241' | head -n1