No, that is often the way that SSDs fail -- the become read only and will no longer write, so you cannot erase anything without the ability to do a write. That is actually a good thing compared to HDDs, as you generally do not lose any files when the end comes for the SSD. A format would also not alter the files in this case.
This is the least common type of SSD failure as far as I can tell, and is due to the end of life of the NAND. Most of the time the controller fails and all data can be lost like with a HDD. This type failure is due to wearing of of the NAND and everything works fine until the drive experiences a sudden exponential increase of reallocated cells. It is less commonly seen with high quality NAND and very good controllers due to better wear leveling. Some drives will go beyond a petabyte before this happens.