Symptoms: all threads in BackgroundScheduledPool busy, lot of tasks in replication queue, none of the tasks is executing. 

![Screenshot from 2021-04-16 16-21-44_](https://user-images.githubusercontent.com/1549571/115193796-e767d600-a0ec-11eb-887c-5c9c2412e50c.png)

Related to #16895

Possible workarounds (poor options): increasing the background_schedule_pool_size to huge values, or restart server every time when that happens etc. - 

{
        part_check_thread.enqueuePart(part_name, delay_to_check_seconds);
    }
    CheckResults checkData(const ASTPtr & query, ContextPtr context) override;
    
    bool canUseAdaptiveGranularity() const override;
    int getMetadataVersion() const { return metadata_version; }
    /** Remove a specific replica from zookeeper.
     */
    static void dropReplica(zkutil::ZooKeeperPtr zookeeper, const String & zookeeper_path, const String & replica, Poco::Logger * logger);
    
    static bool removeTableNodesFromZooKeeper(zkutil::ZooKeeperPtr zookeeper, const String & zookeeper_path,
                                              const zkutil::EphemeralNodeHolder::Ptr & metadata_drop_lock, Poco::Logger * logger);
    
    std::optional<JobAndPool> getDataProcessingJob() override;
    
    
    bool canExecuteFetch(const ReplicatedMergeTreeLogEntry & entry, String & disable_reason) const;
    
    bool executeFetchShared(const String & source_replica, const String & new_part_name, const DiskPtr & disk, const String & path);
    
    void lockSharedData(const IMergeTreeDataPart & part) const override;