It's my understanding that the SW points are tied to your rapid rewards number and not to the credit card.
This is correct. They are not held by Chase but by SW Rapid Rewards and are deposited into SW rapid rewards monthly at statement end.
However, the reward points would expire after a certain time period if you did not accrue anymore
Yes. They will expire in 18 months or so I believe if you have no activity in your Rapid Rewards account. You can always buy the minimum amount of points to keep the points active though.