Like with mechanical HDDs, it depends on what "dead" means.
If "dead" means "there are lots of bad LBAs and the drive locks up or stalls when reaching a certain point", then yes, you can still erase some/most of the drive. If "dead" means absolutely no I/O works to the drive, BIOS doesn't see it, etc. then no, there's no easy way to erase the contents of the drive. You could open the drive up and short out the NAND cells, but this would void your warranty and kill any chance of an RMA.
You're going to have to trust the company you bought the SSD from to not "steal" your data. I've yet to read of this ever happening though (with any company, SSD or MHDD!), so I'm of the opinion it's just paranoia.
If you have confidential data of the severe sort (e.g. PII, etc.), then you should be using an encrypted filesystem. Linux offers this, FreeBSD offers this, Windows 7 offers this. Use it.
