Can my parents claim a deceased adult child as a dependent?

Your parents can claim him if he met the requirements for being a dependent. If they claim him, they do not have to file a return for him.

If your brother had no income in the year of his death, no tax return needs to be filed for him. The fact that your brother died does not prevent your parents from claiming him as a dependent in the year that he died if the tests for claiming him as a "qualifying child" or "qualifying relative" are met. The relationship test for being a qualifying child is met because your brother was a child of your parents. The remaining tests are as follows: (1) Your brother had to be permanently and totally disabled before his death because he was over the age of 23; (2) Your brother had to have lived with his parents for more than half of the time he was alive during the year; (3) Your brother could not have provided over half of his own support during the year; and (4) Your brother could not have filed a joint return with a spouse for that tax year (unless that return was filed only to get a refund of income tax withheld or estimated tax paid). The first test for being a qualifying relative, is that your brother was not a qualifying child of your parents or anyone else. If he wasn't permanently and totally disable, he won't be the qualifying child of your parents or anyone else. If he lived with your parents for more than half of the time he was alive, then he can't be the qualifying child of anyone other than your parents. Your brother meets the second test, member of household or relationship test, because he was a child of your parents. The remaining tests include: (1) Your brother's gross income for the year had to be less than the standard exemption ($3,800 for 2012 and $3,900 for 2013); (2) Your parents must have provided more than half of your brother's total support for the year; and (3) your brother could not have filed a joint return with a spouse for that year (unless that return was filed only to get a refund of income tax withheld or estimated tax paid). Your parents should review this with their tax return prepare and claim your brother as a dependent on their tax return if your brother qualifies as their "qualifying child" or "qualifying relative." If they have already filed the return without claiming him, they can file an amended tax return to claim him as a dependent in that tax year.