I suggest you stop checking for your back links. You should judge your performance by what happens in the rankings and what happens to your bank account. Most backlink checking services use different sources of information and none will be close to the index that Google maintains. Forget about checking backlinks, it will only serve as a deterrent to your overall goal. This is coming from someone who focused quite a bit of time on indexing links over the past few years.
I think its not possible when Google crawl back link and back link is broken means website expired, not work, not found type error, than you bet wrong behavior in search engine.
Instead of struggling to remove your bad backlinks, you can focus on getting better quality backlinks.