i know that US currency is actually a textile, not paper-- it's 25% linen and 75% cotton. not sure about social security cards, but there is precedent for using fabric and other textiles in the creation of government documents, and it's specifically to make them more durable.
It just feels like very sturdy paper. There may be denim involved in the making of it but you absolutely can easily tear them. I've had to replace one before when it got torn accidently