Please forgive this re-post. I could not edit my previous question to make it clearer.
My brother is PoA for both my parents and only filed their 2005 tax return in Dec 2008 or Jan 2009 (they left MA in early 2006). He did not correctly account for the cost basis of their 2005 stock trades so MA is taxing my parents on the TOTAL of the trades, not just the total trades less cost basis. Last February, they started garnishing my parents' social security. Is there a deadline for amending their returns, or is there any remedy for these two, elderly (81 and 82 yo) people who have no other source of income?

You can amend the returns anytime. Further, since the return was filed LATE (DEC 2008 or JAN 2009), you can still amend the 2005 return and claim any refund that was not originally claimed.

Given that your brother botched it the first time, you should hire a local, experienced tax professional and have him/her prepare the amendment. The tax professional may also be able to help you STOP the garnishment.

Further, Massachusetts should NOT be able to garnish their Social Security benefits unless their net worth is such that the garnishment will NOT affect their standard of living.