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. - 

{
    if (!getSettings()->remove_empty_parts)
        return;
    auto parts = getDataPartsVector();
    for (const auto & part : parts)
    {
        if (part->rows_count == 0)
        {
            ASTPtr literal = std::make_shared<ASTLiteral>(part->name);
            
            dropPartition(literal,  false,  true, getContext(),  false);
        }
    }
}
void MergeTreeData::rename(const String & new_table_path, const StorageID & new_table_id)