First of all, your son shouldn't be responsible for protecting himself from an 11 year old boy who is probably twice his size. That is your friend's responsibility when she is taking care of him.... period. The problem is your friend's inability to control her son. I worked with severely emotionally disturbed boys for 8 years in a group home. It was my responsibility to keep the younger/smaller boys safe from the bigger ones when they got angry.
First of all, when one of the boys did get out of control I was capable of handling them physically. I was trained to know how to restrain them to keep them safe and other's safe. If your friend's son is severe like this she should get that training. Residential treatment facilities sometime train parents and foster parents these skills.
Another point is that I was stronger and more dominate than all of the boys and they knew it. This fact is important. If your friend's 11 year old son feels more dominate than his mother and uses aggression to control her, thats a problem. The kids I took care of knew I wasnt scared of them. Some emotionally disturbed/behavior kids use their anger out bursts to control their parents and others. They know their parents cant handle them when they get out of control so they get their way and they make their parents walk around like they are on egg shells all day long. Some parents are scared of their kids... even at 11 years old. If this is the case, the 11 year old is in control when he becomes angry not his mother. If this is the case, you should find a new babysitter. Well at least until your friend learns how to parent her son's special needs.
As for your son if you choose to keep allowing your friend to watch him. Tell your son to never be alone with the 11 year old boy. He should be within sight and sound of your friend at all times and when the 11 year old boy gets angry, he shoud instantly stop what he is doing and go sit beside an adult and let them know what is going on. He shouldnt say anything or try to do anything to control the older boy.
As for your friend, you need to have a VERY serious talk with her aabout her son and her inability to meet his needs. I'm not saying that you have to be mean but you do need to ask her what she is doing to protect your son when her son gets angry. There needs to be a plan that she knows to follow and you know also. For example, it should be HER responsibility to keep your son within sight and sound at all times. Its good to tell your son this, however, its ultimately your friend's responsiblity especially if her son is physically aggressive.
Basically, your friend needs be the one doing something to protect your son. If she cant do that, keep her as a friend however look for another babysitter.