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. - 

++suspicious_broken_parts;
                return;
            }
            try
            {
                part->loadColumnsChecksumsIndexes(require_part_metadata, true);
            }
            catch (const Exception & e)
            {
                
                
                
                if (isNotEnoughMemoryErrorCode(e.code()))
                    throw;
                broken = true;
                tryLogCurrentException(__PRETTY_FUNCTION__);
            }
            catch (...)
            {
                broken = true;
                tryLogCurrentException(__PRETTY_FUNCTION__);
            }
            
            if (broken)
            {
                if (part->info.level == 0)
                {
                    
                    LOG_ERROR(log, "Considering to remove broken part {}{} because it's impossible to repair.", getFullPathOnDisk(part_disk_ptr), part_name);
                    std::lock_guard loading_lock(mutex);