Second, if I understand your question correctly, you're concerned that your assessment is low--that you may have lost all your equity in your home and that the comparables may reflect "walk aways." You're not going to like this, but: (1) It's probably true. Your home probably has dropped sharply in value. (2) It would be a very unwise decision to try to get your assessment raised. The assessment is used for tax purposes. The higher the assessment, the higher your taxes. It's not going to raise the true market value of your home by a penny, even if you do appeal and get a higher assessment. The only thing that'll happen is that the taxes will go up on a home whose value has dropped. That's not a wise decision.
Third, tax assessments are not an accurate reflection of a home's market value. Where I live, for example, the tax assessor says it considers an assessment "accurate" if it's in the low 90% range of accuracy. So, for instance, a property actually worth $400,000 could be assessed anywhere from about $365,000 to $435,000 and my local tax authorities would consider it accurate. And recognize that not all assessments are accurate. Your jurisdiction may have somewhat different parameters; you can call them to find out.
As for what homes they consider, again, it's up the jurisdiction. But, generally, yes, they should be comparable. Usually, that means geographically close by, roughly same square footage, same number of bedrooms and baths, maybe roughly the same age. But often they will include short sales and foreclosures. After all, those are real sales. And if you put your home up for sale, you'd be competing against nearby comparable short sales and foreclosures. So it's not unreasonable if those are included in the comparables.
If you really want to know the value of your home, either ask a Realtor to run a CMA for you or pay an appraiser to do an appraisal. That's not the purpose of an assessment.
And getting back to the assessment, there'd be nothing to gain and real money to lose if you appeal a low assessment, asking for it to be raised.
Hope that helps.