Condolences on the loss of your parents. 
You'd have to contact Synchrony to find out for sure, but my gut instinct is that they won't do it. Discover does--I know that from personal experience--but I can't imagine Synchrony transferring cards like that. Besides, they should have been notified of your parents' deaths when they occurred. The fact that the account is still open means they don't know your parents are deceased, and that's not good. I'd get that taken care of ASAP, and in the process casually ask if they can transfer the card to you.
FWIW, my experience with Discover was completely different, i.e., I was not an AU on the card nor did I have any other ties or connections to the account. I was simply contacting Discover to let them know that my mom had died, and to close the account, when out of the blue the CSR asked if I'd like it transferred to me. With its perfect history from 1991 on my credit reports. Of course I said yes!
Good luck, and I do hope you'll post an update. Some of us have been wondering if other banks transfer cards upon the cardholder's death, so this would be a good data point.
@Murph5065 wrote:I am a AU on a gas card that was opened back in 2006 by my parents, they both have passed away now and the account is still open but i do not have a card anymore, is there anyway i could possibly get a new card to continue using the account for gas? The account is 16 yrs old the balance is showing $0 on it. It is through sychrony.
Sorry about your parents.
You'll just have to call Synchrony and see what they're willing to do for you.
@Murph5065 wrote:
@SouthJamaica wrote:
@Murph5065 wrote:I am a AU on a gas card that was opened back in 2006 by my parents, they both have passed away now and the account is still open but i do not have a card anymore, is there anyway i could possibly get a new card to continue using the account for gas? The account is 16 yrs old the balance is showing $0 on it. It is through sychrony.
Sorry about your parents.
You'll just have to call Synchrony and see what they're willing to do for you.
I just talked to sychrony and as long as i can verify the SS number for both parents listed on the chevron gas card and it shows me as AU they said they could let me have the account to take over for gas card. Yehaw
Awesome.
I wish I had as fine a keepsake to remember my folks by! 
