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. - 

broken_parts_to_remove.push_back(part);
                }
                else
                {
                    
                    
                    
                    size_t contained_parts = 0;
                    LOG_ERROR(log, "Part {}{} is broken. Looking for parts to replace it.", getFullPathOnDisk(part_disk_ptr), part_name);
                    for (const auto & [contained_name, contained_disk_ptr] : part_names_with_disks)
                    {
                        if (contained_name == part_name)
                            continue;
                        MergeTreePartInfo contained_part_info;
                        if (!MergeTreePartInfo::tryParsePartName(contained_name, &contained_part_info, format_version))
                            continue;
                        if (part->info.contains(contained_part_info))
                        {
                            LOG_ERROR(log, "Found part {}{}", getFullPathOnDisk(contained_disk_ptr), contained_name);
                            ++contained_parts;
                        }
                    }
                    if (contained_parts >= 2)
                    {
                        LOG_ERROR(log, "Considering to remove broken part {}{} because it covers at least 2 other parts", getFullPathOnDisk(part_disk_ptr), part_name);
                        std::lock_guard loading_lock(mutex);
                        broken_parts_to_remove.push_back(part);
                    }
                    else
                    {