Yes, nearly all the A-kasse offers also an additional wage-insurance. But it is NOT supported by the danish state, and therefor you have to pay more (its like a normal insurance). Its called "Lønsikring". We also have an article/comparison of Lønsikring on our site.
The page on our site is here: https://a-kasser.dk/lønsikring/
But try to search on Google for Lønsikring. Also normal insurance companies offers this product.