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 profit minus losses. 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 contact a local, experienced tax professional and have him/her prepare the amendment.