always into the surge protector.
The reason is pretty simple. If you did not plug into the surge protector, and you had the dreaded lightning strike hit your home, the surge would flow through the power cord, into the amp of the sub, out through the signal cable back into the suboutput of the unprotected receiver.
Unprotected receiver, because the outputs of the receiver would not be protected by the surge protector.
There are separate "sub" surge protectors. The idea is that your sub may be located a long distance from the main surge protector. Personally, any decent $25 surge protector with the built in line conditioner is all you need for the sub.
What component failed in the past? The sub or the surge protector?